Here you assume that the father has acknowledged that it is his child and that the child can have his name.

If the father left the woman even before the child was born and he has no more contact with the 2 of them , well , I guess that you can say that " the father has deceased ".

For some women it may feel like that.And it is sometimes easier to explain to the child , why the father is not there.

Well , just my 2 C....