In private, Prof is my lover, we agreed on that. Never discussed it with Kip.
I was taught to introduce people by the relationship and name eg. colleague Joe, work friend Eric, neighbour Sue, cousin Jane etc.
So, this label thing is a struggle, I am currently going with either just name or friend + name.
Like others said, if the person being introduced knows me well enough, then they know I have 2 lovers, so they only the need the name. If they don't know then "friend" will suffice.
Me: mid 40s female. currently in a monogamous partnership with;
Mr Dom: late 40s. 1 year.
Prof: recently ended open relationship.