change name of an illegitimate children

Atty., good pm.!
I am a mother of two children and they are not carrying the name of their father because we are not married and that made them illegitimate. We separated ways after 5 years of living together. After 3 years I learned that the father of my children landed a job in Canada. How could I ask for their support if they are not using their father's name? Their father also failed to sign the acknowledgment of paternity, if I will ask him to sign just this moment I know that it is not easy. What will I do so he will be oblige to give support to my children.

Please help me what to do...

Thanks...

just like i advise those whose partners are in the USA, i recommend you look for a group in Canada who will provide you with legal aid.