Like you, we registered them in his name as we always said we'd get married one day and my name would become his too.
I really regret this and would advise ALL unmarried mums to register the baby in THEIR name and NOT the dad's.
Anyway, fast forward to us splitting and me hating the fact that they lived with me and I had to deal with school, dentist, doctrs stuff by myself and was sick of being called mrs X (didn't mind so much when we were together, as if we married that was who I'd become nyway).
So, he did not have PR at that time as it was not automatically given but he was applying for it. In meantime I changed their name to mine, with help from a solicotor (who said he can contest at any time). Had a while all with same name and it was nice.
But, he objected and in the end, we had to agree through solicitors to compromise - double barrelled name which is what they are today.
Would I do it again? No, not fair on the kids.