The father of Christopher William Bradshaw-Isherwood was Francis Edward Bradshaw(-)Isherwood, b. 1869. His baptism record shows him a Francis Edward Bradshaw, son of John Henry Bradshaw Isherwood. Early on, he is consistently shown as Isherwood. At some point, a hyphen was added to his name and he became Bradshaw-Isherwood, but even then, he was sometimes shown as Isherwood. His son Christopher was baptized as as Christopher William Bradshaw-Isherwood, but he later shortened his name to Isherwood.
I have entered Christopher's LastNameAtBirth (LNAB) as "Bradshaw-Isherwood," with his CurrentName as Isherwood. I think I should add his father with the LNAB of Francis Edward Bradshaw Isherwood, with the CurrentName as "Isherwood-Bradshaw." Does that sound reasonable and correct?