If the father name is not put on the birth certificate can the mother still go for child support?

Yes, even if the fathers name is not on birth certificate she can go to the local Child Support Enforcement & open up a case against him. It helps if you know the SSN, last or current job & last or current place of residency. This will help them move faster in getting what is owed to your child. If you don't have all or some of the information it will take longer. Hope this helps.