The Duke and Duchess of Cambridge have announced their newborn son is to be called George Alexander Louis. He will be known as His Royal Highness Prince George of Cambridge.

The announcement at 6.20pm showed the couple have chosen to stick with very traditional royal names. There have already been six British monarchs called George – the last being the Queen's father, George VI. Louis is also a favourite and was the name of Lord Mountbatten, the uncle of the Duke of Edinburgh.

The announcement comes a day after the duchess left hospital and two days after she gave birth, and hours after the Queen met her great-grandson for the first time.

George was the most popular name with betting firms William Hill, Coral and Paddy Power. James was also a favourite with punters, with Alexander, Henry, Louis, Richard and Arthur the next most popular choices.

It was widely expected that William and Kate would not wander far from convention and select anything too outlandish for a prince who is likely to reign one day and whose name could symbolise an era.

The naming has happened quickly by historical royal standards. Prince George's father was not named for a week, and it took a month for the name of the baby's paternal grandfather, Prince Charles, to be announced.

Earlier, for the first time in more than a century, a reigning monarch met a great-grandchild born in direct succession to the crown when the Queen was introduced to Prince George.

She made the short journey from Buckingham Palace to Kensington Palace, where the Duke and Duchess of Cambridge and their son had spent their first night at home as a new family.

Not since the birth in 1894 of the eldest son of the future George V and Queen Mary – the future Edward VIII, who later abdicated – in the twilight of Queen Victoria's reign has such an encounter occurred. Though Wednesday's meeting lasted just 30 minutes – before the start of the Queen's traditional summer break at Balmoral on Friday – it adds another footnote to royal history.

Arriving in a dark green Bentley, the 87-year-old monarch was alone: the Duke of Edinburgh was at Windsor, where he is still convalescing following exploratory abdominal surgery last month. She had previously said she was thrilled with the safe delivery of her first great-grandson, who was born at 4.24pm on Monday weighing 8lb 6oz in the private Lindo wing at St Mary's hospital at Paddington in west London.

Among other visitors received by the Cambridges was Prince Harry, the baby's uncle, who is now bumped down to fourth in the line of succession. He has previously said: "I can't wait to be an uncle."

The duchess's sister, Pippa Middleton, visited on Tuesday night shortly after mother and baby were discharged from hospital.

After presenting their newborn to the world in a photocall on the hospital steps on Tuesday, William and Kate will now seek some privacy. After the Queen's visit, the duke, duchess and infant prince left Kensington Palace for Bucklebury, Berkshire, where the Middletons have a manor house.

A Kensington Palace spokesman said: "This is now a private and quiet time for them to get to know their son." Details of the meeting with the Queen, therefore, are unlikely to be made public.