The thing is the she's part of much longer bit, he didn't bring her up just to shit on her.

The whole special opens up with Ari complaining people wasting his time with annoying conversations and the fact that he still can bring himself to avoid them or ignore them.

Ari's shitting on things that annoy him, but he's also shitting on himself for pretending like he's paying attention even though he really want's to walk away.

Yes, if he didn't mention her by name it would have been much much less cruel....but for better or worse Ari's whole schtick has been about being someone who mocks sensitivity...although in this case not mentioning her name probably wouldn't have affected his persona here.

( Unfortunately, mentioning her name was probably necessary for a joke that good laughs...I'll explain later )

To be fair, he does make a point to say...

" she's not even that annoying... we just have nothing in common " So, obviously its still hurtful , but I can't agree that he wrote as a 100% attack on the woman...

As for her arm, he uses it to get laughs, but he doesn't shit on her for having one arm... in fact he explains why he mentions it.

In my opinion, a big reason why this story is getting laughs is that fact that he's again annoyed with himself for feeling the need to mention her one arm.

... all he wants to do is complain about how annoying she is... but because she has an obvious tragic injury it would be weird not to mention it... which further annoys him...because now it sounds like he's an asshole, shitting on one handicapped person !... which is even more frustrating because he's the real victim here and he's just trying to vent about how his this woman rapes his time !

" she has one arm... it's got nothing to do with story....I'm only telling you because if you ever saw her you'd be like wait... I dunno is that her or not ? because he didn't mention the part about the one arm, so maybe it's not its her ? That's the only reason why I'm telling you ! It's not why she's annoying if that's what you think...I knew her when she had two arms ! "

Also mentioning the one arm led to the big pay off line of " one day her arm to annoyance just shot the fuck up "...which got a pretty good laugh, especially for the first 5 mins.

The part about about being fat and smelly was the cheapest shot by far. It's just a blatant insult if you are on the receiving end. He also could have left her out it at this point, because it was just a general segway to a short rant about smelly fat people... ( aside from the visual of her washing w/ one arm )

Why I think he chose to specifically mention her name

I'm pretty sure that it was simply of matter of crafting the wording of the joke to make it work on stage.

Without mentioning her name, the setup would go something like this:

" I was talking to this girl, a los angeles comedian.... she's so annoying...we never have anything to talk about, also she has one arm " A one armed comedian is pretty ridiculous and without her name it makes the whole bit sound like a badly made up story about a fictional fat woman with one arm...

If the audience doesn't believe the story from the start, every mention of the one arm is probably going to get eye rolls and scoffs instead of laughs.

Yea, maybe he could have said something like, " I was at the comedy store, talking to this los angeles comedian... she's soooo annoying... In the ne ee