Queen Elizabeth II visited with her new great-grandson, George Alexander Louis, Wednesday at Kensington Palace for the first time, before William and Kate took the royal baby to visit his maternal grandparents in Bucklebury.
The baby will be formally known as His Royal Highness Prince George of Cambridge. George is the queen's third great-grandchild and the third in line to the British throne.
Prince Philip, who is recovering at Windsor Castle after exploratory abdominal surgery last month, did not accompany the queen.
Afterwards, William, Kate and the baby left the palace in a Range Rover, bound for the home of Kate's parents Michael and Carole Middleton.
William is taking two weeks' paternity leave from his job as a Royal Air Force search-and-rescue helicopter pilot, and palace officials said he and Kate would now spend "private and quiet time for them to get to know their son."
Bookmaker William Hill had George -- the name of six previous British kings -- as the favorite at 2-1 odds, with James at 4-1.
Images of the prince, his little hand peeking above a white crocheted wrap, blanketed the front pages of British newspapers Wednesday. The Daily Mail offered a photo album image with the headline "Baby's first royal wave.
The prince slept through his debut public appearance -- though William assured the media he had "a good pair of lungs on him."
The Associated Press contributed to this report.