Every notable musician with Berklee ties is a drop out: Melissa Etheridge, John Mayer (IIRC), I’m sure I forgot many more.
Do composers count? We learned of a few heavyweights in my film music seminar course back in my undergrad.
Wikipedia has a full list of Berklee alumni. Yes, some of the graduates are very notable. The most famous names I saw on the list were Joe Zawinul (Weather Report), Branford Marsalis, Al Di Meola, Quincy Jones, Pat Metheny, Paula Cole, Bill Frisell, Susan Tedeschi, John Scofield, Brad Whitford (Aerosmith), and Gillian Welch. I recognized the name of a couple of film composers in there, too. So there are a lot of famous jazz players who are not big rock stars, even if they’re very influential in their own genres, but there are also some singer songwriters and more straightforward musicians. Quincy Jones is better know as a producer than as a musician, but if he’s not notable in music, few people are.
Those aren’t all graduates, though. If I understand correctly the OP is looking for notable musicians who managed to go to Berklee for 4 years and not move on or get snapped up before graduating. I can’t access the reference that Wikipedia uses at work but I think the Berklee website is defining “alumni” as “passed through our doors”. I suspect the list of musicians you may have heard of that actually graduated with a 4 year degree would be much shorter.
Steve Vai is the first name that came to mind. IIRC, a lot of metal guitarists in the 80s jad degrees from the place, though perhaps not of the 4-year variety.
The Wikipedia list tries to make the distinction. So the most famous musicians who appear to fit the OP’s specs (graduated) are:
Jeff “Tain” Watts
…and for many of these, “famous” only extends to the jazz world. YMMV.