I don't know from experience, but your bub will think whatever arrangement you're living in is "normal", and won't worry about it nearly as much as you. Don't break up with your new man because of this - no matter who you end up with or when, you'll have to figure out what to say about his father at some stage!
Is your partner prepared to take on fatherhood repsonsibilities? He must be if you're living together. And if so, won't he in fact end up being a daddy in the truest sense of the word - by caring for your boy day to day?
You'll need to decide what you want your son to know about who his genetic father is, and I guess it will depend on whether the father is still involved etc. There's not much point trying to explain something so complicated until your son is around 2-3ish, so just take it as it comes, and try not to worry!
This new forum is strange ...