The norm reflects the attitude that someone's name represents them as a person rather than some role of theirs. It is therefore seen as more respectful to use this form of reference wherever possible rather than "reducing them to their role".
Pretty much all norms like this are culturally determined with just-as-strong-arguments being available for doing it some other way, but if you want to play basketball, you have to learn the rules of basketball, and if you want to exist within some particular society...
Within this norm, one introduces the name ("my girlfriend Emma") and expects the other to either remember Emma is their girlfriend or to be able to fake remembering that Emma is their girlfriend (the latter is a major part of the norm).
It's also the case that not using the person's name signals keeping your interlocutor at a distance, equivalent to "I wouldn't want to introduce you to this person", which in informal workplaces is seen as rude. For you as the person who does not have a direct relationship with Emma, it's not inherently disrespectful to the girlfriend to fall back into the anonymous mode of reference ("you said your girlfriend was on a vacation?") but showing that you remember the name is a social signal that you care about your coworker.
There are much more complicated regional/socioeconomic/cultural variants and subtle shades on all this, of course. Among my father's family, given names aren't common in reference, but all references to shared relatives -- even among adults -- are given not relative to the speaker, but to the audience ("your cousin" instead of "my sister", "your father" instead of "my uncle"). This is much harder to do than you'd think if you didn't grow up doing it!