Law schools don't seem to care very much about staking out original names. Consider two Orange County law schools: Irvine University College of Law (founded in 1993), and the University of California, Irvine School of Law (which should start accepting student applications this fall). Imagine the confusion that will follow when local attorneys start saying, "I graduated from Irvine."
That is not to say that the presence of two "Irvine" law schools will cause consumer confusion—the acid test of trademark (or, as here, service mark) infringement. Any prospective law student would sort out the two schools long, long before applying for admission. Clients and members of the general public, who don't care so much about such things, might get the two "Irvine" schools mixed up, but that would probably not give rise to an actionable infringement claim.
Note, too, that there seems to be no bad intent. Irvine University first opened in the city of Irvine, only later moving to its present home, in nearby Cerritos. And, of course, nobody could plausibly claim that U.C. Irvine School of Law adopted its name to poach on its predecessor's good will.
The two "Irvine" law schools will thus probably have to learn to live and let live. It that, they'll join such law schools as John Marshall (Chicago) and John Marshall (Atlanta); University of St. Thomas University (Minnesota) and St. Thomas University (Florida); and Washington University (Missouri); University of Washington (Washington); and George Washington University (District of Columbia).
Unlike those schools, granted, the two "Irvine" schools will share the same geographic market. New York Law School and New York University School of Law share that fate, though, and appear to coexist quite happily. It perhaps helps that the latter goes by "NYU"—a strategy that U.C. Irvine might do well to emulate. It that event, Orange County would have not two "Irvine" law schools but, in effect, one named "Irvine University" and another named "UCI."
[Crossposted at Agoraphilia, and MoneyLaw, and College Life O.C.]