Shel had similar fears, and even during the pregnancy she worried and worried that Jazz would 'reject' her as mum, or resent her in some way... but as soon as Jazz was born she fell in love!
Theres actually a pic of when Jazz was minutes old on the warming table thing, holding Shel's finger, and thats pretty much been them two summed up! Shel also held Jazz for the two hours after the
c/s, doing the skin-skin thing when I was in recovery, which I think was great for bonding.
Theres no question that we are both mums, and when I hear the garage door opening in the afternoon I yell out "Mummy's home" and Jazz gets all excited, her legs kick and she starts laughing, looks at the door just waiting for Shel to walk through, and her eyes just light up as soon as she see's her other mummy!
Of course, possibley try and train your partner in how to make the baby stop crying because thats a pretty big issue for me, Shel just hands her back (but then, thats universal to pretty much all new parents apparently!).
As for names, don't stress. We didn't have Jasmine on our list until the final weeks of the pregnancy, then it came to us and yeah, it was perfect! Our little Jazzy Jazz! So don't worry, you will find one!