If a band has one, and only one, iconic member, they can get away with using the name with only that member. Mark Knopfler could be performing with a second-grade choir and call it "Dire Straits" and get away with it. However, if there's more than one iconic member and only one iconic member is in the current lineup, they cannot legitimately use the name. I don't care what the fuck the papers say, Axl, we both know it's true. Call up at least Slash and then we'll let you get away with it.
If all the members are relative unknowns, or more than one are iconic, then the band should be at least 50% original members, or at least 50% members who have recorded on at least one successful album under the band name. (Therefore there could be a theoretical band made up of Mark St John, Vinnie Vincent, Eric Carr, and Bruce Kulick, assuming one knew how to resurrect dead members, who would have every right to call themselves KISS if there was no band with a higher qualification (eg, Gene and Paul) calling themselves that. It would be better to call themselves The KISS Superfly Experience, though.)
If the band is named after someone (or someones) in the band, the name applies as long as this member (or these members) are present. Fleetwood Mac has been through, in addition to some minor personnel changes, three major lineup shifts, with Mick Fleetwood and John McVie being the only constants. They could play by themselves and get rid of everyone and still call themselves Fleetwood Mac.
If the band is not named after a member but everyone assumes it is, and that member dies of AIDS, then it is proper to add "+ [replacement member's name]" when touring with a shitty fill-in from Bad Company.
If a band is named after an iconic member, who happens to be the brother of a lesser band member, but they rotate lead singers like a guy with a spastic colon rotates underwear after eating at Taco Bell, and finally get all assholey and fire the other member to replace him with the iconic member's son, then rule #6B applies, no matter how good any members may be. The text of rule #6B follows in its entirety: "Fuck you, Eddie Van Halen."
A corollary to the first rule: if there are two iconic members and one leaves but the band still enjoys some success with only one iconic member, that iconic member will be all that is required from that point forth. For example, the iconic members of Journey, to most, would be Steve Perry and Neal Schon. Steve Perry left in the 1980s, but the band had some success without him for a while. This means they can now put out any shit they want under the Journey name as long as Schon is involved.
*--For behavior unbecoming anyone, perpetrated in real time over an extended--AH, FUCK IT! MORE MALIBU, BITCHES!!