When my (long distance) girlfriend asked me to be her boyfriend, I asked what that would mean exactly. She said she didn't know, but that she wanted to call me that, so we agreed to just keep it honest and talk openly and figure it out as we go. We have now been together for over three years. She recently started seeing someone else (which I encouraged, as I'd rather see her happy than held back from any experiences she may want, and I never did try to push monogamy on her), and we're still a thing, and we're keeping things honest and talk openly about stuff.
While I'm sure your relationship will be an entirely different journey, I do suggest asking her what the label "boyfriend" means to her, and figure out together what principles you both would like your relationship to be built upon. Make sure you're both on the same page. That's essential. Relationships fall apart when people have different ideas about what the relationship is and why, or when they get bitter about having defined a relationship in a way that turns out not to work for them.
ETA: I'd also suggest establishing that you can revisit the relationship principles together at any time if either of you feel like they need tweaking.