Only 'evidence' I could find was via https://www.gro.gov.uk/gro/content/certificates/login.asp for the Son, Edward, b. 1859.
But is that 'evidence'? Do Registrars demand 'proof' when recording Births? Doubtful. I mean, the answer given might well have been 'Kennedy', and that might well be true - why would she not give her real name?
Not much, sorry (I'm not great searching for records in Ireland, North or South), but it's 'something' I guess.