How about "Benny and the JETs", lol..."McHale's Navy"...Fantastic Five..
That 86 team had Bill Walton, Sichting, Scott Wedman, Sam Vincent, Rick Carlisle and Greg Kite....I even vaguely remember David Thirdkill having a decent game or two for us.
The 08 Team had PJ Brown, TA, Posey, Eddie House and Scal.
2012-13 team has Green, Jet, Sully, AB or Lee, Wilcox and Darko.
If I were ranking them, I'd give that 86 team a slight nod. Bill Walton played out of his mind for us that year.
But I agree with the OP - they deserve a nickname.