Back in 1964, there's a naming tradition that was put forth for the Royal family.
“The King's descendants other than those with the style of Royal Highness and the title of Prince or Princess or female descendants who marry would carry the name of Mountbatten-Windsor.
Archie and Lilibet the two children to Meghan and Prince Harry, weren't bestowed the the Prince and Princess titles or HRH at birth but after Queen Elizabeth's death in 2022, they became eligible for the titles.
After Lilibet’s christening in March 2023, it was confirmed that Archie and his sister had been given the titles of Prince and Princess.
Recently, Meghan and Prince Harry relaunched their website from Archewell.com to Sussex.com.
They were then confirming the change of their children's last names from “Mountbatten-Windsor” to Archie and Lilibet Sussex. This then was the act that breaks the naming tradition which dates back to 1964. It has been quoted above.
According to the now defunct SussexRoyal.com which is Harry and Meghan's old website, the Sussexes would not actively use their HRH titles as they will no longer be working members of the family but they will maintain their titles of Duke and duchess.
The Times reports that Prince Harry and his wife, Meghan Markle, actually switched to the Sussex name after King lll's coronation in May 2023 but had not yet updated Archewell.com with the information.
This accounts as another big step in their lives right from how their own relationship began as a hardship considering the fact that Meghan was not a royal and Prince Harry was not allowed to marry her. They still went through the marriage and made a decision to stay together no matter the hardships which they indeed met.
Following their “forbidden” relationship, some of Prince Harry's rights as a royal were taken away from him hoping for him to get back and get himself into a not forbidden marriage but he still did not oblige.
They went ahead to welcome children into their lives and now with the change of last names it is crystal clear that they are pushing forward the reality they face each single day of being together.
Prince Harry confirms that this is not an act they intend as a negativity or disrespect to the Royal family because they will keep their Duke and duchess titles just that they could not keep the other titles as they are not working members of the family.