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LONDON -- The Prince of Cambridge is off to his maternal grandparents' home in the English countryside today, after first being introduced to his great-grandmother Queen Elizabeth II. But his name is still a work in progress.

The British media showed Prince William and Duchess Kate left with the baby for her parents' estate in rural Bucklebury, about 50 miles outside London. Again, William was driving the Range Rover and Kate was in the back with the baby in a car seat.

The new little prince spent his first night at his parents' small apartment-cottage at Kensington Palace, where Kate's siblings, Pippa and James Middleton, visited Tuesday evening, according to the Daily Mail and others. Both sets of grandparents visited him at the hospital Tuesday.

But his most important visitor so far was the queen, and she came to him, driven the short way over from Buckingham Palace this morning. She spent about 30 minutes with the new family.

For the time being, what we know about the new third-in-line to the throne, first child of the Duke and Duchess of Cambridge, is that he will be HRH Prince (insert name here) of Cambridge. But that's it.

British reporters speculate there might be announcement before the queen departs for her annual vacation at her Balmoral estate in Scotland on Friday.

When Will and Kate left St. Mary's Hospital on Tuesday with their baby, Will said they would have a name "as soon as we can."

And grandfather Prince Charles and his wife, Camilla Duchess of Cornwall, told the assembled media and well-wishers outside the hospital that they had no idea what the child's name was.

A source with knowledge of the matter told London's Evening Standard newspaper that the happy couple have "a number of names in mind, but they wanted to see his little face and get to know him first."

A number of names have emerged as likely contenders at bookmakers, including George and James, but it's not clear whether the royal couple will opt for a traditional-sounding name or break with protocol and go for something more unusual.

According to the BBC, it took a week for William's parents - Diana and Charles - to announce their newborn's name in 1982, while the Prince of Wales' name was not revealed for a whole month when he was born in 1948. However, Prince Harry's name was made public when he left the hospital in 1984.

Choosing a name (actually probably four names) that sounds right after the word "King" is more complicated than perusing a list of trendy baby names, and the queen is likely to be at least consulted in the matter of naming the future monarch.

Reporters stationed outside the gates of Kensington Place began tweeting early today when the queen's green Bentley was spotted entering the palace to visit her third great-grandchild, her first great-grandson.

It's not clear how long the family will stay at Carole and Michael Middleton's estate; William has two weeks paternity leave from his job as a helicopter pilot in the RAF in Wales. New speculation in the British media suggested the couple and baby might spend some time with the queen at Balmoral or at one of the smaller residences on the estate, including Prince Charles' house Birkhall.

Meanwhile, the baby's great-grandfather, Prince Philip, hasn't yet met him because he's still at the royal Sandringham estate in Norfolk where he has been recovering from abdominal surgery. He's expected to join the queen at Balmoral.

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