Using known donor that lives with me..birth certificate, welfare, laws to be aware of?
I'm not sure all the legalities where you are, but in order to just apply for WIC, we have to list anyone in the household- so I would imagine it wouldn't even matter if he was on the birth certificate, you are going to have to include his finances when you apply for any kind of aid, because he is in the household. But you should check for your state (and maybe even federal). Good luck with the birth of your baby!
Forum crashing ... Welfare, etc. probably aren't going to care about your sexual orientation or about how exactly his DNA made its way to yours to create the baby. All they'll see is that you live with your baby's biological father and are raising the baby together. So his income may get counted, depending on how your state does such calculations. If you put him on the birth certificate you can probably count on getting treated like any other unmarried mother living with the baby's father--however that happens to work in your area. The other alternative would be to keep his name off the birth certificate and list him as an emergency contact in appropriate places, although just having him in the same household can make a difference for some things too, as noted above. You didn't mention a same-sex partner. If you have one, or if you get one in the future, and she wants to adopt your child, having him on the birth certificate would probably complicate matters, but I don't know a lot about that.
In CA if you put the the biological father's name on the birth certificate then that gives him certain parental rights and responsibilities. If you apply for assistance - WIC, housing aid, childcare aid, etc, the state will go after the father named on the birth certificate to get him to pay child support.
If you do not want to share parental rights with this person, consider signing legal papers that allows him to act as a guardian in an emergency, but do not name him as a parent.
As an adoptive parent (open adoption), only my and my husband's names are on the birth certificate. Neither of the bio parents names appear there, even though we have one as an emergency contact on dd's school emergency form.
I agree with several posters. If you're co-parenting, he is a parent. Typically he-parents are fathers. Things would be murkier if there was another person parenting. For food stamps, regardless of family status, people who prepare food together are a family in Ohio. My family is a family of 2 and a family of 4 for medical purposes. For TANF, I believe they will pursue child support or include his income if you go for that one in the US.