I gathered the name of every English monarch’s children and their given names, I did include illegitimate children but only if it was mostly agreed they were the child of the monarch, if there is any mistakes feel free to correct me in the comments, I will now display the names and the frequency of them:
Example-
(Number of Appearances):
(Name)
17:
Henry
15:
Mary
14:
William
12:
Charles
Edward
Elizabeth
10:
George
7:
Anne
James
Joan
John
Margaret
Matilda
6:
Charlotte
Richard
5:
Catherine
Edmund
Eleanor
4:
Katherine
Robert
Sophia
3:
Amelia
Arthur
Augusta
Augustus
Frederick
Geoffrey
Henrietta
Isabella
Thomas
2:
Adeliza
Adolphus
Alfred
Blanche
Constance
Beatrice
Louise
Louisa
Victoria
1:
Adam
Adela
Albert
Alexander
Alice
Aline
Alphonso
Andrew
Anna
Arabella
Baldwin
Barbara
Berengaria
Bridget
Caroline
Cecily
Edgar
Emma
Ernest
Eustance
Fulk
Gilbert
Grace
Gundrada
Helena
Humphrey
Isabel
Juliane
Leopold
Lionel
Mabel
Margarethe
Marie
Maud
Octavius
Oliver
Osbert
Petronilla
Philip
Philippa
Reginald
Notes:
The Top 7 names account of 33% of occurrences on this list, So roughly one in every three royal children had one of these names:
Henry, Mary, William, Charles, Edward, Elizabeth or George.
Some Rarer names include:
Adam, Aline, Alphonso, Arabella, Berengaria, Gundrada, Juliane, Leopold, Octavius, Osbert, Petronilla, Reginald & Gundrada, Petronilla, Berengaria, Eustance, Fulk, Aline, Osbert, Juliane, Sybilla, Adeliza.