If you don't consider yourself in a relationship with this man, then paint me purple, strap on a joybuzzer, and call me Jimbob. Because you're in a relationship. This loser is not just a roommate.
If you think he is, or you're letting him call you a roommate with benefits, then you're being used for sex AND as a free babysitter. He has no business allowing his daughter (niece-to-adopted-daughter, apparently) to call you "Mommy." You have no business allowing it either.
She only has ONE Mommy and that's the mother who gave birth to her (even if she no longer sees her Mommy... one day in the future she very well might and that woman alone deserves to be Mommy). Instead, in her very short life she has had to call three women Mommy, including the ex-girlfriend that your non-boyfriend allows his TWO year old to still spend days at a time with.
Daddy is pawning off his little girl on every woman he can find except her actual Mommy. When she comes back from Fake Mommy #1's house, she's difficult to handle. When Fake Mommy #2 has a fight with Daddy, she's difficult to handle. Hmmm, I wonder why?
This is a bad, bad, bad, bad situation. If that "man" has two daughters then I really fear for them and how they're going to grow up. If YOU have a child, I fear for what you're allowing them to witness. I sincerely hope you have ironclad birth control. And a plan of getting out of that place.
EDIT: You know what, in your other post you stated that your bed-buddy's daughter was still having sleep-overs for days at a time with her adopted mother. You never clarified if that adoption was legal or verbal, by the way, you only stated it to boost your post somehow. ANYWAY that doesn't sound like a woman abandoning this little girl.
If you've been around "almost a year" and you don't consider yourself in a relationship with this man in spite of being his bed buddy and doing EVERYTHING a couple does and co-parents do, you're fooling yourself. It's semantics and this guy is a creep for not owning up to the terminology. But until you marry this guy and adopt that little girl you don't get to let that little girl call you Mommy.