There was widespread speculation that Diana would be included in memory of William's late mother.
Kensington Palace announced the name two days after the baby was born.
The name is in line with the public opinion and bookies' favourite. Bookies had predicted Charlotte and Alice as their favourite names for the princess, followed by Olivia, Victoria and Elizabeth.
Meanwhile, gun salutes in London marked the birth of the baby.
Volleys fired by soldiers in Hyde Park and the Tower of London honour the arrival of new royal babies and were last fired when Prince George was born in July 2013.
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They are accompanied by the Royal Artillery Band and their 71 horses pulling six World War One-era Ordnance Quick Fire 13-pounder field guns.
A Kensington Palace spokesperson said: "The duke and duchess are hugely grateful for the messages of congratulations they have received from people all over the world.
"It means a great deal to them that so many people have celebrated the arrival of their new daughter."
Among the first visitors to see the new princess at Kensington Palace on Sunday were her grandfather Prince of Wales and his wife Camilla, Duchess of Cornwall, and Kate's parents - the Middletons.
Kate's parents, Michael and Carole Middleton, and sister Pippa also spent some time with the princess.
Prince Harry, who narrowly missed the princess' birth after returning to Australia to finish his secondment to the country's military, said his new niece was "absolutely beautiful" and he could not wait to meet her.
Queen Elizabeth II is to meet her newest great granddaughter and fourth in line to the throne by the end of this week.
The new parents remain at their Kensington Palace home and will be travelling to their country home, Anmer Hall, on the Queen's Sandringham estate in Norfolk this week.