If I'm not legally yet divorce and got another woman pregnant, can I put my name on my baby's birth certificate?

Question Details: I married my wife 4 years ago. We moved while I was in the Army and lived together until 2 years ago. Then she committed adultery and left to live with her mother elsewhere. I left the military about 8 months ago and moved back home to be with a new girlfriend but have yet to be legally divorced. My girlfriend is now pregnant (and my wife knows and seems okay with it) so a contested divorce does not seem like the route we will be going. As far as putting my name on the baby's birth certificate if there is going to be an issue and if I will not be allowed to because of my being separated but not legally divorced to my wife?

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