I say no. Then you'd have The Green Hand, TheGreenHand, Th3 Gr33n Hand, etc. etc. etc. It'd obviously be much worse with big gangs. It'd be hard to tell if your gang is really taking a town. Also, how would moderating work? Delete the base somebody just paid 130k for? Or change the name to "Generic Gang 83"?
The name list wouldn't be a problem if you could have more than one base per gang.