My daughter was almost 3 and my son almost 1 when DH and I got together. They both almost immediately started calling him Daddy. Neither of us had ever said anything about calling him Daddy...they just did it. I wasn't going to stop them, he is/was their Daddy. More than their bio dad.
I think as long as you aren't forcing them to, then it's ok. They've never called him by his name. I actually introduced him as "Bo" (his name). They always said "HEY!" up until they just decided to start calling him daddy. lol