it depends. I think to use the name they have to have a certain number of the original members (and be free of legal encumbrances between the members). The Pointer Sisters had one. Plus her daughter and her niece.
Dennis DeYoung had some sort of fallout with the rest of the band. There are other members of Styx who still tour as Styx. Dennis goes by his own name but he does all the Styx hits.
The Orchestra (they play ELO) has only one of the original members of ELO, but they don't use the name. Not sure if that's due to legal disputes or because they don't have enough original members.
All the bands I have seen at ETTB have had at least one original member. The Sounds Like Summer series are all tribute bands (no original band members).