just wanted to "second" some of the sentiments expressed upthread, particularly
Judge,
Aspergirl4hire, and
Slithytoves.
I can understand how applying a certain term or vocabulary to your situation may feel helpful, as it can often impart or help create meaning for your experience. but, like some others have said, those labels are often ambiguous and mean wildly different things to different people, so the experience itself is what ultimately matters.
there are many, many possible reasons for why he may not want to use the term "boyfriend"--past hurts, fears, resistance to a commitment, just not that invested/interested, not willing to stop entertaining other future possibilities, etc. Heck, I would cringe at someone calling me their "girlfriend" because I simply don't like the term (I prefer "partner"). And even if you asked him explicitly, well, he could (sadly) lie, or not even know his own reasoning well enough to articulate it fully or honestly.
So, like others have suggested, I would try to figure out whether the experience of the relationship itself is satisfying for you, and whether or not it feels good to/for your soul. If it does, you might ask yourself, what would using this term add to it? The answer may happily be, "Well, not much, things are great."
(If it turns out that your answer is something more like, "It would make me feel safer and more secure in my relationship," that would seem to me to be an indicator of a different and perhaps larger issue, beyond simple terminology.)