What will you tell your kids when they ask or want to know about who fathered them?
The truth, of course.

I only ask as my sister in law has no name on her birth certificate for 'father' and she has found it hard to deal with in her life particularly when questioned by employers etc about it.
I have never ever had an employer see my birth certificate, I can't imagine why this would be necessary, and what business it could be of theirs to query an employee's parentage.