When I was 12, there was a song by Everything But The Girl that made a lasting impression. These were lines that leapt out at me: "You must give your child a name some time. Well you mean his and what's wrong with mine? Yeah, what's wrong with mine?"

The record was called Mine, and lay well-loved (and scratched) on my bedroom floor. I'm not sure the songwriter, Tracey Thorn intended to radicalise 12-year-old girls, but somehow those lyrics implanted themselves – and 20 years later, when I came to name my first child, they resurfaced.

Our daughter was to have my surname rather than her father's. Radical, huh? You wouldn't think so, would you? Not in this enlightened, post-Mad Men age of (alleged) sexual equality. But apparently, yes – while hyphenations of both surnames are becoming more common, it is still rare for a woman to pass on her surname when it is different from the father's. According to one survey, just 4% of women do this, and a cursory glance around the globe hints it is not exactly common practice elsewhere.

In the Netherlands, the woman's name is used before a man claims fatherhood. Both the father and mothers' surnames are passed on in Spain and Spanish-speaking countries, but the father's name is more often used day-to-day. Occasionally, however, the matrilineal name sticks: Pablo Ruiz y Picasso used his mother's name, Picasso, for example. This usually happens for snobby reasons (basically, the mother's name packs more punch).

Still, this mass compliancy baffles me. Surely, more women want to carry on their family names? Surely, we don't hate them so much (do we)? Yet the truth is that when I took this route, I had no idea that I was socking it to The Man. I had no idea I would be in such a tiny, kick-ass minority.

My reasons were a mixture of the personal and the political. On a practical (and emotional level) my children would be the last bearers of a family name that I happen to rather like. History is important to me, and seeing as one branch of our family line traces back to Dorset, it made me sad to think that hundreds of years of Hardys would come to an end. Meanwhile, my partner's ever-expanding Whittaker clan (already boasting four grandchildren and spanning two continents) would carry on its inexorable march to world domination. Then there was the stubborn part that thought, why should they automatically have their father's name? How sexist, how outdated is that?

Luckily, my partner Andrew is an enlightened soul, who also likes a quiet life. I've been told a more alpha male-type would have put up a fight, that apparently this is a "huge deal" that very few men would go along with it; that I am a ball-breaking bitch.

Looking back, I can't remember any particular conversation that sealed this apparently huge deal, when I metaphorically cut off his goolies – and neither can he. So I sit him down with a long stiff drink and ask him how he feels. Honestly.

"I'm happy with the situation," he says, "It just felt natural that the children would have your name – we aren't married and we've never been very conventional. You gave birth to them and carried them inside for nine months. It just seems fairer that they get your name."

What about hyphenation? "That seems clumsy, as if we're trying to sound posh. And then there's the whole issue of whose name goes first. I mean, the whole idea of losing your surname and taking on someone else's – it's what women who get married are traditionally expected to do, but it's a very strong symbol of a women subjugating her identity to a man."

I know! Wonderful, hey? But do you feel I have emasculated you, I ask. He laughs. "Maybe throughout history men needed that extra bind of the name to make them more responsible and connected, but it just seems vain, egotistical and old-fashioned these days. I suppose I am less visibly attached to my children in a sense because they have your surname – maybe there is a tiny fear that it may cause problems some day – being frisked at border controls or something. Anyway, I put equal weight on my mum's side of history as my dad's. For me, our children are about us, as people now. It's not the names of our fathers that count."

For the very modern couple though, not content to toe the patriarchal line, plumping for a surname can be a fraught affair. Child and family psychotherapist Nicola Dyson says it is becoming another area to be navigated – alongside who empties the bins or who "marinates" their career. "Families are changing," she says. "They are much more fluid than they were in the 50s, say. So it's hardly surprising that our children's names are changing too."

That both parents are happy with the choice is essential; she says, but sometimes it is the wider family who are distinctly unchuffed. "If there is hostility," says Dyson, "the most important thing is to keep it away from the children and don't make their name a battleground. It is their identity, their sense of self."

Luckily, Andrew and I agreed, but for others it can be tricky. "My parents-in-law were really upset when I chose to give my daughter my surname," says 40-year-old Jill, who lives in Sydney. "They just couldn't accept it. Gifts would arrive for her addressed to their surname, not mine. They thought it was against society that Amy had my name, and that it was a man's right to name his child. I mean, what century are we in? Who carried her for nine months and is her primary carer? That's my view but certainly not their's."

In the end, Jill feels her decision was vindicated when her marriage broke up after she discovered he was having an affair. "Now I am the one with Amy almost 100%, so I certainly feel I made the right decision," she says.

This underlines a controversial point that Dyson makes, that "giving the child the mother's surname may make sense because while not wishing to denigrate the importance of the father, statistically it is the relationship with the mother that is most likely to last." The most crucial factor, she says, is consistency: "It can be very disconcerting for a child if the name gets changed – if the mother remarries, for example."

This may sound cynical – who has kids with someone thinking they are gong to spilt up? And, of course, there are many blended families out there that tick along nicely, but in the course of researching this article I came across a lot of single mums who resent the fact that their kids carry the name of someone they basically detest. "My two children both have the name of my ex, and I have always hated the fact they have a different name to me – especially as their dad has not really been an integral part of their lives," says 42-year-old Clare from Manchester.

"I've found myself looking back to when I first had them and they had my surname on the hospital tag – just for a short period of time. It made me happy. When signing forms at school I have always had to write 'mother' in brackets at the side so they know who I am. I didn't enjoy that. My worry now is that if I marry my current partner and take his name that I will have the same name as his two children, whereas my two would be different. I would hate for them to feel left out."

Thirty-nine–year-old Jenny, from Lancashire, managed to change her and her kids' surname back to her maiden name after her marriage spilt up. "I did it through the court. It cost £250. You need consent from the father, but as he failed to attend court they ruled I could change their name in his absence. It was really straightforward and my children were over the moon," she says.

Thankfully, my situation is far more straightforward. For one thing, I have never encountered hostility, but I have certainly had some baffled looks. One friend pointed out that they're all male names anyway, so what was the point? Well, yes, but you've got to start somewhere, I said. Another friend argued that by giving the child the man's name, you are compensating for the fact that he can't give birth. Cue the whole bonding argument, which I think is an insult to Bugaboo-wielding dad's everywhere – that by giving children the father's name, Daddy is less likely to run for the hills when the whole horrible, nappy-smelling paraphernalia of parenting kicks in.

But I've had positive responses too – plenty of "God, I wish I had done that!" – but some deeply empowered women, always ready to fight their corner for equal pay, have got a bit eye-rolly, as if I am doing something irrelevant, just to make a cheap point. I disagree.

While I don't think the female line should always be passed on – it's boring and monolithic whichever sex routinely trumps the other – wouldn't it be nice if there were more of a mix? I think it is a tremendous injustice that the male line is still automatically passed on – that it is a visible and etymological sign of the sexual inequality that our country is steeped in. And, without wishing to get too drum-beaty, I am glad that my kids' names aren't such an obvious manifestation of this.

And, on a more prosaic level, I just like the name Hardy. Laurel and Hardy, Nancy Drew and the Hardy Boys – smart, dippy and up for adventure. Just the kind of name-baggage we like.

A father's view: 'I just thought it was right'

I have two daughters, aged two and four, and they have their mum's surname. It goes without saying that my wife, on marrying me, kept her name – but that's not unusual these days. Older children or adults decide to adopt their mother's last name (Marilyn Monroe, Barry Manilow, Ryan Giggs), but again that's a bit different.

I've realised that giving children the matronymic surname at birth is rare. Come to think of it, not a single one of our friends has done it (without doing the double-barrelled thing), though of course we're far from being pioneers or alone.

Why did we decide to do it? It wasn't a "we" decision: I said I thought it was right, and my pregnant girlfriend agreed and was pleased (we got married after both kids were born). If I say it was because I am a staunch feminist, fighting bravely against patriarchy, that makes it sound far more thought-through than it actually was.

It's true that it didn't seem right to me that children should necessarily take their dad's surname (which seemed an old-fashioned idea), but it wasn't ostentatiously done – it seemed quite natural. I was so delighted and excited to be having a child, that's all that really mattered.

I looked up a Mumsnet thread on the subject, in which a woman says her partner "would feel less of a man, if child had its mother's name". That sounds hilarious to me.

Is it seldom done because families like surnames to continue – for the sake, as it were, of the family tree? I can understand this, but I can't say I was, or am, so bothered about posterity. Perhaps it also helped that I was nearly 40 when my daughter was born, quite old in other words, and didn't feel I had to please other people.

All of which, poorly articulated, leaves four questions – probably more, but four will do.

One: if I'm such a feminist, why did I get married? I never thought I would, but somehow it stopped seeming part of the old way of doing things, and started to seem like it could be our way of doing things, and not necessarily patriarchal. That's to say, the nature of the marriage – how it was organised, with jobs, etc – seemed the important thing.

Two: would it have made a difference if my first child had been a son? No, the decision was made when we didn't know the sex of the baby.

Three: do I dislike my surname, and prefer my wife's? No.

Four: how did my family react? If my parents were opposed, they didn't mention it – they, too, were simply thrilled I was (finally?) having a kid. And my wife's family? Well, they don't even like the fact that she hasn't taken my surname, so they find it very odd indeed. Her relations address letters to our children using an invented hyphenated surname.

Ah well, it's become a good joke. Besides, the world can only be changed one step at a time.

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