Hi.
As far as I know you can name the father with out his signiture. If you want him to be on there.

I know that if they are on there you can't take the child out of the country with out his permission. I'm not too sure about that if he is in a different country. It's probably something that doesn't matter at all, but I have a friend who just had a little boy & is single & who decided to leave the name off.

Her son will still know his father, but she discussed it with his family & they all agreed with her. She has a 7 year old DD as well.

It's totally up to you what you do.