I've very rarely had something like this happen to me, but when I did I simply introduced them by their name, without any additional info. Or with a characterized title such as "partner in crime" and that way it's loose enough to be friendly while still hinting that there's an undertone of intimacy.

After introducing as such, I make certain to check the person for signs of distress in their behavior and eyes. If I feel that there is some concern, I make certain to initiate physical contact with a deliberate lean into, indicating that I'm not trying to distance myself from them or leave myself open to anybody else.

I've found that this approach works comfortably, avoiding any awkward notions (at least between me and the mate--the person I'm introducing to might be a bit confused, but that's typically the lesser of my concerns). It might not work as well for very touchy people, but those who know me are aware that touch is a boundary I'm not too fond of having people cross, so the lean into thing is a pretty clear expression of my connection with a person.