Originally Posted By: Zed
I think that the lack of name is reflective of the fact that there was a stigma to the child but not to the father. Personally I can think of a few names.
Doesn't babyfather refer to the youth of the parent?

Yes, Zed, and how sexist is that?! The mother certainly suffers stigmatization...
And no, "babydaddy" is as in "my baby['s] daddy", no reference to age.