An introduction works when both people gain a possible next sentence.

A name gives two people nothing to do with each other. What makes an introduction work is a supplied hook: something either of them can pick up without effort, ideally something shared or something the other would find interesting. The host’s job is not the label but the opening line neither of them has to invent while standing there.

Next time you introduce two people, add one sentence about each. He has just come back from the place she keeps talking about; she does the thing he was asking about last week. Then stay for thirty seconds and step away once the second sentence has arrived.