Prince's name: George Alexander Louis

(CNN) -- The Duke and Duchess of Cambridge have named their son George Alexander Louis.

After showing off their royal bundle to the world, the Duke and Duchess of Cambridge are doing what new parents do after the big birth show is over. They enjoy some incredibly sweet moments alone with their baby.

Kensington Palace made an official statement about this development Wednesday, saying that William and Catherine are now down to the business of getting "to know their son."

British media are feverishly reporting where they might be, saying that the couple and child are in the village of Bucklebury, where Catherine's parents live.

Earlier Wednesday, Queen Elizabeth II went to Kensington Palace to see the newborn for the first time. Uncle Harry paid a visit, too, the palace told reporters.

The parents and the as-yet-named, perhaps future King left the palace by car around lunchtime, UK media reported. The couple has been mum about their immediate schedules.

Tuesday evening, though, they brought their baby out of the Lindo Wing of St. Mary's Hospital in London, delighting throngs of journalists camped out for a first peek.

Anticipation remains fevered, of course, because the world doesn't know what to call the new royal.

The prince and his wife are "still working on a name," William said on the hospital steps, "so we'll have that as soon as we can -- it's the first time we've seen him really, so we're having a proper chance to catch up."

Many bets are being placed as the wait continues for the baby's name to be announced. British bookmakers Ladbrokes have George and James as favorites Wednesday, followed by Alexander, Arthur, Louis and Henry.

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