I presume you have the 1841 Census?
James Square,
Edinburgh St Cuthbert, Midlothian
William Begbie, 30, Lapidary
Jane Begbie, 25
THOS Begbie, 1
Whellemina Russell, 15, Female Servant
All born Midlothian
William BEGBIE married Jane Elizabeth VERNON, 13 May 1839, Edinburgh Parish, Edinburgh, Midlothian, Scotland
Brides Father was THOMAS Vernon
(Familysearch.Org)
Seems the liked to rehash Family Names.
Thomas V's Brother Harker John (or John Harker) Gilman Begbie named a Daug Jane Elizabeth Vernon Begbie in 1877.