You will need to treat the child as your own if you marry that man. Not because of that man really or because of you but because a child doesn’t deserve to be a second category child in a family merely on account of an error his parents made. Basically, there would be equality among the children. You’d be closer emotionally or further, who knows. It would be relatively mutual unless either of you shut off unilaterally. But in some core aspects, even though the child weren’t yours, it would be just as well as if. Things like school, college, car, other such expenses, those would be pretty much equal, just like the food you put on the table for everybody.
And it’s not unnatural to fear that a man could favour his first child over the subsequent children with another woman. I guess you might as well ask him how he would treat the children, if he would be able to love and treat the new ones equally. Not all men can and not all men can even get over the first woman, this much is pretty much a fact of life. Now this doesn’t mean your current or prospective boyfriend will inevitably share the attitude. Also, nobody says that the eldest must get everything, as in everything for the first and scraps for the rest. Perhaps it makes sense if there’s money for only one college scholarship or only one person can realistically operate the family business after being handed it down from dad, but otherwise it’s not like the first gets all. At any rate, you need to talk this over with the man. Even without actually having children from previous relationships can people have wildly different, subjective views of family, children, how things are done.
Wouldn’t worry too much about the child not being able to call you mother. You’d need to accept that you wouldn’t be the child’s mother in a “historical” sense or a replacement for one. Just as if some misfortune were to happen and you split up, the children you gave birth to would still be your children. Same with “the other woman”. But this absolutely doesn’t mean you can’t bond and have a meaningful relationship with a child that isn’t biologically yours. Even if you don’t actually enter a replacement parent relationship.
Another thing I noticed is, aren’t you a bit too eager to get out of being single perhaps? Can’t blame you, every once in a while I need to battle the same feelings. But speaking of feelings precisely, do you have them for that man or is it more about having a good catch on the radar? Everybody has flaws and has the potential to bore you to death or annoy you to death. Sometimes, and I guess especially for some people, convenience and good catch does work, but it’s all the easier if you actually have deep personal feelings. Those, I think, should make it easier with that person’s family, including any children from previous relationships. If you don’t actually care for that guy personally but he’s just an objectively great guy and a good catch – which I am not saying is the case – then that’d be reason enough on its own to rethink the idea of starting a relationship with him, even without children in the equation.
Finally, walk a mile in that kid’s shoes! I can’t blame you, I would perhaps feel the same, I don’t know. I generally do tend to look for people without children, without exes in the picture. But I was that kid. I could talk about that for a long time but that’d be a waste of breath. In short, basically, if you find out you can’t warm up to the kid, and I can’t blame you if you, then skip the dad. It would inconvenience you far less, I think, to find a new boyfriend than it would cost the kid to sort things out if he got any impression of being a second category child or especially a problem, in other words, of being unwanted. Which is, by the way, somewhat similar to what you want to avoid for your own children, from what I can gather from your post.
Good luck!