My son has a daughter that carries the name of another man. He hasn't established dna, but we are quite sure he is the father. What are his paternal rights if any?

None.

Being "quite sure" doesn't mean anything.

Odinn is correct he has no rights to that child currently. However that doesn't mean he may not get rights.

ANY question on law needs to include your general locale as laws vary by area. Depending on local laws he may be able to file for custody. The court would then order paternity testing which could establish his rights.

He may (or may not) have rights to determine paternity though DNA and ask for rights if he is the father.

Factors, is mother married to other man at birth.
What county and if US what state, the laws vary greatly