Think you need to look in the 1891 UK Census for a William Morris, tailor and assuming Alfred was already in the army so not at home on the night, you would need to work back from any William Morris, tailor and see if he had a son Alfred.
I don't see a birth in Ireland that suits unless he was registered without a christen name. There are a few Unknown but I haven't looked at them yet.
Yes that is likely the best avenue. Thank you. Alfred joined the army around 1887 or so I’m told based on his service number.