Don't know what to think

When I was 18 I got pregnant with my first. Her dad stuck around and we eventually got married just before my 21 birthday in 2011. We ended up splitting up in January of 2015, because his jealousy issues were too much to deal with. So I met someone in May of 2015 and got pregnant with his child in April 2016. He basically took off right in the beginning. Recently, my ex, the father of my first child has been stepping up without me even asking and helping out so much when I have doctor appointments and asking if I need anything anytime I'm not feeling well. He ended up texting me this last week and I completely broke down at how sweet it was...

He has already told me he knows exactly what that would mean and has even said he would go as far as putting his name on her birth certificate. I've obviously never stopped loving him and we're taking things slow (we're still legally married) so I guess my question is if he were to put his name on her birth certificate and all the sudden the biological dad reappears is there anyway he could have his name removed or any consequences to doing this? Thanks for your help!