With a new play, audiences never quite know what they're getting, but early ticket-buyers for Anthony Neilson's latest piece at the Royal Court were taking an exceptionally wild shot in the dark. Originally advertised several months ago as "Untitled New Play by Anthony Neilson", it was only revealed to be called Narrative on 15 March, three weeks before opening.

Neilson's play joins a very small sub-set of theatre productions that have been delivered onto the posters unbaptised. The other most recent British example was Mike Leigh's 2011 show at the National theatre, promoted and sold for several months as "New play by Mike Leigh", before, at the last minute, becoming Grief.

In both cases, the delay resulted not from indecision or wilfulness on the part of the dramatist, but because the plays were born out of improvisations with the cast. Writer-directors who devise work in this way generally have not decided the theme of the piece or, even if they have, prefer their actors not to know. Clearly, performers walking into the rehearsal room past posters announcing that they were improvising a show called, say, Landing on the Moon – or even Grief – would inevitably be influenced by the words in their work. Although theatres are understanding of these working methods, producers tend to be nervous of promoting a show with no name.

The exact function of the title in drawing an audience is, though, an uncertain science. There are extreme cases where the show's name is an event in itself, winning attention through length and tantalising hints of content. My favourites of this kind are David Grieg's The Cosmonaut's Last Message to the Woman He Once Loved in the Former Soviet Union (1999) and Ntozake Shange's For Colored Girls Who Have Considered Suicide When the Rainbow is Enuf (1975). Using more words in the title than Samuel Beckett employed in the entire texts of some plays, these phrases are hard for a listings browser to ignore – although long names, too, are unpopular with producers because newspaper advertising is often charged by lineage. For either economic or aesthetic reasons, the 2010 film version of Shange's play was truncated to For Colored Girls.

Modern producers and writers sometimes also worry about a name that is too short or bald. The standard practice from the 17th to 19th centuries of christening a script after its central character – Richard III, Hedda Gabler – is now extremely rare, either because of a worry that such titles are too dull or because of the risk of confusion on posters. (Unless the actors are very well known, it might be unclear whether, for example, Michael Jones was the protagonist, co-star or dramatist.) These days, name-plays tend either to be called after an character with an unusual moniker – for example, Harper Regan by Simon Stephens – or offered with a knowing wink: such as Robin French's recent Heather Gardner, premiered by the Birmingham Repertory theatre, which translates Hedda Gabler to 1960s Birmingham.

Simon Gray, when he went eponymous with his 1987 play Melon, had taken the precaution of giving his central character a strange and ambiguous surname, although he was dissatisfied with the play and later renamed it, more melodramatically, The Holy Terror. But productions of the script still stumbled, which may confirm the suspicion (common in Hollywood) that for a project to change titles is often a sign of creative confusion or trouble. Revealingly, Stephen Sondheim's least successful musical has had productions and cast recordings under four different designations – Bounce, Gold!, Wise Guys and, finally, Road Show – although none of these variations gives the uninitiated much clue to the content, which dramatises the early 20th century American entrepreneurs, Addison and Wilson Mizner.

A writer may sometimes prefer a title that withholds or misleads. It's noticeable that, when finally forced to choose a name, Anthony Neilson opted for one that gives almost nothing away. During a period of particularly austere labelling, Samuel Beckett created, for stage and screen, dramas called Play (1963) and Film (1965). But this reductionism works less well in theatre than in film because of the punning presence of an alternative meaning of the word "play", which means that such theatre titles as Doris Lessing's Play with a Tiger (1962) and Martin Crimp's Play with Repeats (1989) are not just simply descriptive.

As a test of the power of titles, imagine an occasional theatregoer or a tourist browsing the current West End listings. One advantage of – and possibly even motivation for – theatre's recent obsession with adapting movies is that many of the names are immediately recognisable: The Lion King, The Bodyguard, Singin' in the Rain.

Among the very few recent new plays in the West End, John Logan's Peter and Alice gives nothing away; it could be a play about a suburban married couple rather than, as it is, an account of a meeting between the real-life models for Alice in Wonderland and Peter Pan. Logan, though, would have almost certainly been unable to allude to either of those famous titles in his own because of trademark and copyright concerns. And it doesn't really matter because, as is common now, that show was sold (and has almost sold-out) on the name of its stars, Judi Dench and Ben Wishaw, just as another current hit was promoted as "Helen Mirren in The Audience", making its title literally secondary.

In those cases, the title is almost irrelevant. If Dench or Mirren ever appeared in The Cosmonaut's Last Message to the Woman he Once Loved in the Former Soviet Union, many ticket-buyers wouldn't even notice what the play was called.