Can you still receive child support from the alleged father if another person's name is on the birth certificate?

No, the father on the birth certificate is financially responsible unless proven that he's not the father by DNA.

About 12 years ago in the state of NJ The court ordered me to pay child support to the biological father (Dna test showed I was not the biological father)
The court called me the psychological father so in the courts opinion I was her father. And like the biological Mother he also drank it away.