So I'm pretty sure you're not going to find some paper discussing the problem as you've stated it here... I think I kind of get what you're looking for, but with no interesting metric to constrain matching, it sounds like you're just trying to arbitrarily pair people together. If that is the case, then you there's no interesting name for the process, it's just "pairing".

As in: one person signs up, put their name in the database, another person signs up, check for anyone in the database, pick some random person or the first person or whatever, and make that pair. Of course, this gets interesting in realtime systems... but that wasn't even in your question