I was very proud back in 1991 to be on USS Topeka (SSN 754) when the University of Kansas made the Final Four that year. The Navy had decided that since Topeka, KS, was only about 20 miles from Lawrence (where the university is at) that the Topeka would be the "namesake" boat for the Jayhawks. They sent a photographer to the boat and got a picture of a bunch of us with a KU banner hanging off the brow as I, a recent KU grad, taught the crew how to "wave the wheat".
This year for the Final Four, there are some "no-brainer" picks for which boats can be the namesake representative. The most obvious ones are for the University of North Carolina and University of Connecticut, which are represented by USS North Carolina (SSN 777) and USS Connecticut (SSN 22), respectively. Since Villanova University is located near Philly, she could be represented by USS Philadelphia (SSN 690) or USS Pennsylvania (SSBN 735). Michigan State University is best championed by USS Michigan (SSGN 727), one of the newly-converted Tomahawk shooters.
I note that the five suggested namesake ships represent the five major types of submarines in the fleet: the three classes of SSN, the SSGN, and SSBN. So who would win in a mythical submarine "Final Five". Of course, I'm biased, so I predict USS Connecticut would come out on top due to her unmatched speed and offensive firepower. In the real world Final Four we have coming up, though, I think the team being championed by the newest submarine, the North Carolina, will come out on top.