Prince George and Princess Charlotte Are Officially Using Their New Last Name

Prince George and Princess Charlotte are getting used to seeing their new last names.

The siblings attended Queen Elizabeth's funeral services with their parents, Prince William and Kate Middleton on Monday. In the Order of Service released by Buckingham Palace explaining the order of events at the Westminster Abbey service, royals were named in the order they would walk in the procession.

Prince George and Princess Charlotte, formerly known as the Prince and Princess of Cambridge, were referred to by their new last names. They are now Prince George of Wales and Princess Charlotte of Wales — as is the case with the youngest in the family, Prince Louis. Their parents go from being the Duke and Duchess of Cambridge to the Prince and Princess of Wales.

The change came on Sept. 9, when King Charles III addressed the United Kingdom for the first time since Queen Elizabeth II died at the age of 96. Charles, 73, shared that Prince William, 40, and Kate Middleton, 40, have inherited the titles of Prince and Princess of Wales.

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The children will see the change outside of official royal functions as well. The children were previously known as George Cambridge, Charlotte Cambridge and Louis Cambridge at school. Now they will be known to their friends and teachers as George Wales, Charlotte Wales and Louis Wales.

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The change comes as all three siblings started at their new school, Lambrook, this week following their family move out of London over the summer. The family of five now lives in Adelaide Cottage in Windsor.

In accordance with the royal line of succession, Charles takes the throne, to be followed by William, who will now be followed by George, 9. Next comes 7-year-old Charlotte, followed by youngest sibling Louis, 4. Prince Harry becomes fifth in line to the throne.

Charlotte's spot in the royal line is due to a 2013 succession law that allows the crown to pass on in order of birth, regardless of gender. (Up until then, succession rules stated that the crown would pass to the eldest male heir and only to a female heir when there were no other male heirs available.)

"That might seem like a minor thing, but it is a big victory for equality," Williams previously said of the amendment. "It says to people, which [the Queen] proved more than anyone, that a monarch is a job and a woman can do it just as well as a man."

As William and Kate take on their new titles, a royal source told PEOPLE the couple is focused on "deepening the trust and respect of the people of Wales over time."

"The Prince and Princess of Wales will approach their roles in the modest and humble way they've approached their work previously," the source added.

As Kate Middleton takes on the title of Princess of Wales, which William's mother, the late Princess Diana, once held, a royal source told PEOPLE: "The new Princess of Wales appreciates the history associated with this role but will understandably want to look to the future as she creates her own path."