I’m paid to do a job and I do it well, they could call me The Equaliser for all it matters (showing my age there)
Oh, I do love a bit of The Equaliser... but back to the point, I’m wondering if this IS the point. OP mentioned that until last year, she actually had “admin” in her job title. Did you perhaps get a promotion that came with more responsibilities and a new job title, but no raise? I’ve found that people who are “paid and paid well” often don’t get upset about what others think of their job title, because the money is more important than someone else maybe getting the title wrong, or not even wrong but lumping you into a group (I still don’t quite understand if she’s calling you an admin assistant still instead of a buyer’s assistant or just referring to you as part of the admin department or something), in internal emails that your clients won’t even see. If, however, all you got from a promotion is the title, you’re going to be very protective of it. I could obviously be wrong; just stating what I’ve seen.
But at this point, OP, you might want to consider that 83% of people think YABU so when you’re bringing it up with your manager and HR, etc., really consider if that’s benefitting you and how they view you, regardless of what they say to your face. Plenty of people on MN are managers and HR staff and directors. Now, if this person is calling you personally by the wrong title to outside clients (as in an actual email that says “blah blah our admin assistant, Mumsnorthernmonkey”), then yes, at that point, I would say you have every right to complain and make a point that she’s probably confusing your clients, too.