This is a complex question. To answer your question, I'll say that, yes, you can put any last name that you want on the birth certificate. Here's where it gets complicated:
(First of all, you don't mention if you are REGISTERED Domestic Partners. This is a very important distinction, as without registration, you are merely GFs and have none of the rights that married people have.)
You could put your faith in the parentage presumption, which says that a child born of two married folks is legally presumed to be the child of both. But the Family Code doesn't actually say that, it says a "husband" is so presumed. The RDP act says that RDPs get "all rights," but if you most to an gay-unfriendly state, your RDP's rights may not be recognized.
More importantly, the bio-dad may be disinterested in the baby now (or even ever) but he is still the baby's dad. If you want to terminate his parental relationship, you'll need to take steps. One thing that you could do would be to file for a step-parent/domestic partner adoption, which would include a relinquishment of parental rights by the bio-dad.
If your DP doesn't want to adopt, then you won't have much luck terminating bio-dad's parental relationship, because the courts want children to have two parents where possible.
The two of you should consider having a sit-down consultation with an experienced family law or adoption attorney.
Legal disclaimer: The response given is not intended to create, nor does it create an ongoing duty to respond to questions. The response does not form an attorney-client relationship, nor is it intended to be anything other than the educated opinion of the author. It should not be relied upon as legal advice. The response given is based upon the limited facts provided by the person asking the question. To the extent additional or different facts exist, the response might possibly change. Attorney is licensed to practice law only in the State of California. Responses are based solely on California law unless stated otherwise.
While I am not an expert in same-sex marriage issues, I would think that you would have to put natural father’s name on the birth certificate. Thereafter, you can use a different last name for your child (i.e. yours or your same-sex partners if you took her name as well). Many people go through life using hyphenated last names, or nick names, not using their real names (i.e. Hollywood, actors, etc…). In regard to the formalities of life, I could imagine that at some point you could file a Petition to terminate parental rights if father has nothing to do with the child for a year and fails to support the child, then contemporaneously, have your partner adopt the child. Once the adoption is completed, you could look into the issue of possibly amending the birth certificate.
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