Ruminations on changing band line ups.

If a band has only a single original member remaining in the lineup, who is not the front man, can that band still refer to themselves by the name they were founded with?  I don't know that I have the answer to this, but it's a question that has been troubling me since I saw the recent Guitar World with Lynyrd Skynyrd on the cover.  At this point in time, Gary Rossington, one of three guitarists, is the only founding member of the band who is still alive.  Yes, Ronnie Van Zant was replaced by his brother Johnny, and current guitarist Ricky Medlocke played drums with the band in an early incarnation before fronting Blackfoot (the poor-man's Skynyrd), but is the band still really Lynyrd Skynyrd? 

Some of the guys in the band now, have been playing with them for about a decade, making them official members of the band.  So, if Gary Rossington dies, does Skynyrd carry on under the familiar Confederate banner?  By a similar line of questioning, what if the original front man - who embodied the overall vibe of the band - is gone, but the other sidemen carry on under the name.  The prime example would be Thin Lizzy.  Phil Lynott WAS Thin Lizzy.  He wrote the songs, his personality carried the band.  So in his passing, the remaining members may be better off calling themselves Thin Lizzy Tribute?

What if Trent Reznor carries Nine Inch Nails for the next 10 years with the exact same lineup, making his sidemen official members of the band, including them in songwriting duties and granting them carte blanche to represent the band individually in interviews.  The Trent decides to call it quits, but the rest of the guys stay together.   Can they still be Nine Inch Nails? 

Farewell Citizens