Examples of the minutiae at issue are things like a person's hometown, the name(s) of their partner(s) and/or children, which, if any, college they attended, occupation, etc. Any piece of personal trivia that could come up in casual conversation.

A person who has this ability strongly might be able to intuit and then recall the name(s) and relative age(s) of a coworker's sibling(s) from a passing comment made years ago to a third party. One who has it weakly might require active study to learn and recall facts about their own spouse and/or children.

"Identity Memory" is a weak candidate that a) is too generic and b) does not seem to be in wide use. I will not reject it out of hand, however; I could be wrong about either or both of my objections to it.