I love this thread!
I would ideally prefer to be able to introduce my partners by their names, plain and simply and not have to explain why I'm holding hands with someone that I haven't exclusively introduced as my bf. But, I live in a very small community. Just getting up and going for a walk with someone of the opposite sex immediately invites questions from at least one person, even when there's absolutely nothing sexual/romantic between us.
So, it gets complicated. I introduce 'R' as my friend, (it's much too early for us to have any kind of bf/gf/lover status) and when my lover 'D' comes to visit, I will introduce her as my friend as well. I also will not refrain from kissing her or flirting with her in public. That will immediately raise confusion and at least a few questions from other people in my community.
That's where I have no idea what to call them or what to say when people ask. If they want to know the truth, I'll tell them, but not without the fear of being misunderstood or rejected.
'R' is someone I'm falling in love with, feel a very, very strong connection with, but I'm not ready to be his gf, so I still call him a friend, not bf. My connection with 'D' is much more clear, simply because she's in a primary relationship with her gf. I am one of her side lovers and we're good friends. I'm happy being called her lover and don't need more from her. I also really love her, but I'm not in love with her.
I would hope that in the future, there will be acceptance when and if I call more than one person my bf or gf.