I would just go using Dad for the new baby for your DP and let you DD decide herself if she wants to start calling him Dad or continue with hiscurrent name. I think your DD won't really start to even make connections about it all until she is around 5yrs old - and when she starts asking questions then just be honest and tell her that she has two dads, but it is up to her what she wants to call your DP.

The other alternative is for your DP to have a diiferent name: Father, Pop, Daddy (rather then Dad), Pa, Da.