If a woman uses an anonymous sperm donor to have a child, who is listed as the father on the birth certificate?
No direct answer to your question, but isn’t this pretty much the same question faced when a woman doesn’t know who the father is because she had multiple sexual partners?
IANAL. It might vary from state to state. Here in Indiana, if the mother is married, the father is the husband, regardless of the biological facts. If she’s unmarried, perhaps, like in Hollywood, the father is Allan Smithee. 
It can often be left blank, or filled with “unknown”. IANAL (I am not a llama. I am also not a lawyer.), but the exact procedure undoubtedly varies by state.
I’m almost positive that here in Maryland the woman, even if she is married, does not have to list a father. I’m not 100% on that as they asked some really strange questions, but I thought that was one of them.
Father: *Undisclosed * (State of Maine)
In Ontario: Wilt Chamberlain.
I’m sure they just say something like “father unknown”.