If SHE lists him unknown then this falls to her not you. You do not have to prove that she doesn't know who the BF is. In all honesty if she doesn't know who he is then fine, list unknown...but if she does and SHE doesn't list then it's her fault. She is going to be only one listed and then that falls to only 1 parent's parental consent to be terminated and that's all that needed.
In Lousinana there is the Putative Father Registry:
http://www.dhh.louisiana.gov/offices...52&detail=7812
which means that if he thinks he got someone pregnant he must register when the registry. I do not know how it works in LA but here in TX if someone saying that they are a certain child's father within 30 days of birth then their rights are automatically terminated (they must know the city/and hosptial where the birth took place).
If I were you I would give the ball to the BM and if she lists him fine...if not...well...then...it's not liek you know the name of the BF and can say hold on...you need to list so and so...
But once the adoption is final it is final...no one can challenge it...