OK…my daughter is doing grad work “there”. I refer to it the way I always have…“Penn. My daughter is at Penn”. My husband says no one calls it that. Its called “U.Penn”. Which is it?
Penn.
Unless they were in the business school, in which, IME, they say Wharton more often than Penn.
No alum/student/faculty says UPenn. In conversation, they may say University of Pennsylvania the first time for clarity to avoid confusion with Penn State. 
Penn is official per the University’s style guide
"“Penn is the registered mark of the University and is used on stationery, web pages and as the primary substitute for using the full University name in publications and other external communications,”
Penn (I do say Wharton if I am in a business situation).
Not my alma mater, but Penn is standard.
Disagree with @skieurope on the “no” (and in bold, too!) one saying “UPenn.” I’ve heard it from other alums; I’ve even used it before (with people who I think will think I’m talking about Penn State if I say Penn).
That said, Penn is the most common (and “correct”) answer. I chose whether to say Penn or Wharton depending on who I’m speaking to). I very rarely say “University of Pennsylvania” in its entirety.
I graduated from Wharton in1991, I say “Penn” or “The University of Pennsylvania” (if I think they might confuse it with Penn State), never “UPenn”.
Is this just about Penn?
If not, the University of Michigan is called “U of M,” never “UMich” people! Where did that come from?
Well, the question was posed in the Penn forum. 
Edited to save myself from going behind bars :))
@ChoatieMom I too thought the question was in general, what do you call your alma mater. If ppl are viewing “latest posts” @skieurope they may not note what forum it was originally posted in.
The OP is clearly referencing Penn in her opening post. That said, there is nothing stopping a user from opening a generic “What do you call your alma mater” thread in the cafe to handle questions about University of Michigan, University of Chicago, and other colleges where alum seem to cringe when others refers to their college “incorrectly.”
Ok…