She may be passive aggressive or she may be just awkward. I’d tell her, once, very clearly and calmly, that her continued emphasis on my shopping was uncomfortable and that I’d prefer that she drop it. Expecting her to read my mind on the subject makes about as much sense as pretending I could read hers.
I definitely don’t think she’s awkward, definitely feel it’s a mean girl type of comment.
Since I no longer spend much time with her, I’ve heard comments that she gives off a mean girl “insider” feel which I didn’t get when I was an “insider”.
I am not a person who needs to be popular, never was, don’t need to be in my 50’s.
I’ve tried in the past to be funny and shrug. Oh well, that’s ok, I do like to shop. Who cares. But now that we aren’t close, it comes off mean. And seriously, who cares at this age what anyone else does. It doesn’t define me.
Yep, she’s mean, and for whatever reason, she’s targeting you. I would be inclined to give no response whatsoever to her next provocation.
I don’t remember the exact context, but something I owned came up in conversation once (someone else brought it up) and another woman in our group said a sarcastic “Must be nice.” I tilted my head, looked her in the eye, and said “I like nice things.” Not in a humorous way to gloss it over, but unapologetically and clearly making it the last word on the subject. And @deb922 exactly – who cares what someone else does, especially now that we’re so far (theoretically) beyond middle school? 
I don’t think she’s baiting you. I think she’s using you, thinking she’s somehow charming others or winning points by putting you down. (In effect, she is, whether or not you do like shopping.)
She’s focusing on one point, not an accomplishment or asset or even just a fact, “Deb, who lives on Elm Street” or “Deb, who manages the XX project.”)
I would not be inclined to let it go. A friend specializes in how women communicate (how we not only accept insinuations or putdowns, don’t stand up, but do it to ourselves in how we self present.)
Tell her. Be direct. Nip it. For all of us women. Sure, you can find a nice way.
When someone says something rude, I think it helps to put it back on them. I’d say, “Why would you say that?”
I agree I’d tell her. Something like, “Hey, I am a friend and really am not interested in always being called Deb who likes to shop.” If you like, you can introduce me as, “Deb, who loves trying the latest great restaurants,” so we have a conversation starter and we can talk about some of the cool eateries in town or something.
I would socialize with the other women in your friend group one-on-one or in smaller groups that for whatever reason don’t include the mean woman. Life’s too short to spend it around people who want to bring you down. Now that I’ve had a milestone birthday I feel justified in being picky about who I spend time with.
I wouldn’t swap shopping for dinner, either. Something about you that doesn’t come across as lightweight. (I don’t mean anything’s wrong with dinner, just that this gal isn’t being friendly in limiting you that way.) It’s different if it’s a new person you do share an interest with: “Deb, who also likes to golf” is making a potential connection, if the other person also plays golf.
“Jane, I’d prefer if you simply introduce me as Deb. I’m more than shopping and can express my own interests.”
Good idea, @lookgingforward. I would definitely express this and then hope she listens. If not, I’d keep my distance from her. Life is too short to hang around with folks that make us uncomfortable and disrespect our repeated requests.
@deb922 the snark in me wants to tell you that when you have her and the other friend in your car later this week beeline to every shopping strip you drive by saying “I just want to stop and shop for for a minute!” MAKE. HER. LIVE.IT. 
LOL - Is it possible she had a moment of anxiety/brain-freeze and forgot your name? (then went to her go-to topic). I’ve been guilty of that kind of thing, trying to cover with general description - “this is Tommy’s mom”
I agree with @juniebug
In this case I might look perplexed at her and ask, “Why do you ALWAYS say that?” Since it’s become a pattern/habit
It’s hard to do this, though. And you have to just say that (and nothing more) and look her square in the eye. If she says, “What do you mean?” then I’d say something like, “The last three times you have introduced me you have referred to my shopping habits. Why do you do that?”
I’d say something like: “As a matter off fact, I do like shopping. However, this is not important now and I prefer a different introduction. So, let’s pretend this never happened and try again”
When you describe this woman in post #16, it sounds to me as if you just don’t like her very much. You didn’t say anything positive about her friendship. If that’s the case, the next time she makes a comment about your shopping, stop her and let her know you don’t like it. I wouldn’t try to laugh it off. It bothers you, so let her know. What have you got to lose?
Really, post 16 says a lot about OP. Agree on the fact that you are not friends. Leave it at that. Don’t waste time on each other. There certainly isn’t any kindness or tact on show here.
It does sound like this woman has some baggage and perhaps some jealousy or other unhealthy emotion towards you, @deb922 but I really think in most situations the direct approach is best. She may, truly, have no idea that her frequent references to your shopping irritates you. I really try (not always successfully) to assume good will. As a few others have suggested, at a time when I was alone with her, I’d let her know that you feel uncomfortable with her frequent references to your shopping. You can highlight the example of the introduction. Hopefully, she really wasn’t aware, will apologize and stop the behavior. If she doesn’t, then you know more definitively what type of person she is and can make a decision about whether she fits in your life, etc.
Sometimes all you need to do is looking at her for a moment silently, then turn to the other woman and say you can call me Deb.
I think the silent non reaction can be quite effective.
I like that @eyemamom
I won’t do anything overt. We are in the same group of friends and there is no need to confront things. I don’t want to make things awkward with our friend group because I’m the one who will lose. No one wants 2 people in a group to fight.
I will try and jokingly say something that will let her know that I’m not super pleased. And only if she brings it up again. Maybe she got that I wasn’t happy at our last encounter. Since I don’t plan on spending time alone with her, I’m not really interested in getting in a little fight about something so trivial. But I’ll be firm if it’s brought up again that I’m so much more than what she keeps bringing up.
Thanks to everyone who commented, it was very helpful
If you can manage a bemused and sardonic silent look…