So there are different types of record longevity we are talking about here. The Royal Artillery Band has had the same name since 1557, but it has had many personnel changes. It has the same name, and perhaps plays many of the same charts, but is it really the same band, since the members are all different?
There has been a Kingston Trio since the late fifties who play much of the same materials on the same type of instruments, wearing the same type of shirts, but none of the original members are still in the group.

ZZTop, on the other hand have been the same three guys since 1969. Is there any group that can beat that record?
FloraG said that she meant the same people.