I would let it evolve naturally, perhaps gently encouraging a different but still fatherly nickname (Pop? Papa FirstName?) if "Daddy" becomes confusing.
Oddly, my stepdaughter's mother, years ago, told my husband it would be OK for their daughter to start calling me "mommy" (she's "mama"). To me, it seemed WAY too soon to be heading down that road (we were not yet living together, not engaged/married/otherwise life-partnered yet, though it was clear we were heading that way). So I never encouraged it, and my SD didn't start.
Now, occasionally she'll call me Mom (especially if she wants something
) but that's come organically. She may or may not start calling me more by "mom" names when the baby's here and we're encouraging him to call me "mommy" (listening to my SD babble nonstop about "mama" as a toddler made me utterly not want to be called that myself). We'll see. Your DC#2 might start something like that, too, in which case I would neither encourage nor discourage it.
In response to a previous poster--I don't think an actual adoption is necessary (my husband's stepsisters have called his father "pop" since he married their mother, even though they were never adopted and their biological father was somewhat in the picture and is now deceased), but I do see your point. Do make sure the commitment's there and for the long haul.