Leroy, if you haven't heard I'm starting a trend to call it just 'The Octagon.'
Feel free to join me.
I used to think that was a good idea, but then I found this page:
http://www.terraserver.com/samples_sports_ncaab.aspIt has aerial photos of 91 NCAA basketball arenas, including Bramlage. 18 of these arenas are octagons.
Assuming this is a random sample, this means that almost 1 in 5 NCAA basketball arenas are in fact octagons. At the very least, Bramlage is not unique in its shape. Suddenly, "The Octagon" doesn't seem like such a good nickname.
"Octagon of Doom" is marginally better, as it differentiates Bramlage as the only octagon where you will almost assuredly meet your doom. Okay, it's a little cheesy, but now that it's picking up steam, it will be tough to change it.
I'll try anyway. Might I suggest,
THE CAGEIt's short, catchy and ominous-sounding. It evokes MMA, which is often fought in octagonal cages. It conveys the idea that once you step inside THE CAGE, you're in for a serious pounding. It also could mean that THE CAGE is where rabid Wildcats may be found, so you better be prepared if you're going to get inside.