I have committed what seems to be the "ultimate sin" and referred to Penn as UPenn in my first supplement three times and my second supplement once. I guess from all those times I had to keep people from confusing Penn State and Penn "UPenn" became what I used normally. Should I email the office of admissions and tell them this and that it should be changed?
UPenn is fine. The school refers to itself as UPenn in the application.
As a general rule, it's okay to refer to the school by the same abbreviation the school uses to refer to itself.
Can you refer to a prestigious Ivy league college using the abbreviated name of a large state university in the same state, particularly one that is still working its way through a huge child sex abuse scandal? Not so much. If I did, I would work.