I Googled and while I haven't yet found the surname explanation, this site shows Joan FItzHugh married to John Scrope but with their children using both the Saxby and Scrope surnames.
https://freepages.rootsweb.com/~dearbornboutwell/genealogy/fam7278....
Henry Scrope's Wikipedia page only lists these children:
https://en.wikipedia.org/wiki/Henry_Scrope,_4th_Baron_Scrope_of_Bolton
Scrope married, around 1435, Elizabeth Scrope (his fifth cousin), who was a daughter of John Scrope, 4th Baron Scrope of Masham. Scrope died on 14 January 1459; his widow survived him until at least 1498.[1] Their children included:
John Scrope, 5th Baron Scrope of Bolton
Richard Scrope of Bentley (d. 1485), who married Eleanor Washbourne of Wichenford, and had nine daughters.[10]
Margaret Scrope (d.1496), who married John Bernard, Lord of the Manor of Abington, Northamptonshire.
Their son John is linked to this Wikipedia page and he's not listed as John Saxby:
https://en.wikipedia.org/wiki/John_Scrope,_5th_Baron_Scrope_of_Bolton
I'm looking for primary sourced documentation of the parentage of John Saxby, as he appears to be an ancestor for me.