Grammy Grammy, what world do you live in?
The days of the Home Secretary bring present at the birth of royal children ended in 1926, after the Queen was born. Theresa May, Home Secretary, when Prince George was born confirmed that the convention had firmly been left in the past.
The Duchess of Sussex would have had medical care thoughout her pregnancies and medical attendants present at the birth, all of whom can confirm both pregnancies and birth.
Royalty, like anyone else can call their children what they like, although they have tended to stick to more traditional names. However Princess Anne has grandchildren called Lena, Lucas, Mia, Savannah and as more of the late Queen's grandchildren marry I expect they too will also choose less traditional names.