<p>I think that ‘U Penn’ is used in situations where the university might get confused with something else, or by people otherwise not familiar with Penn, much like Chicago U or Tokyo U, both which also share the names of the respective regions they are in. </p>
<p>In the University of Pennsylvania wider community, it is definitely referred to as ‘Penn’ these days, something which was cemented when the university itself formally espoused this nickname some time ago. Back in the day, I believe it was occasionally called ‘U of P’ as someone else mentioned, and I want to believe it used to be referred to simply as ‘Pennsylvania’ as well. </p>
<p>I think the name ‘U Penn’ survives outside Penn’s own academic community since it is unique to Penn, whereas the name ‘Penn’ is a common last name, sounds like ‘pen’, could be short for Penn State, etc. </p>