|Source: Mike DIN NYC-|
I guess this a Doors cover band that calls themselves LA Woman. Which of course is one of the most famous and popular songs that was created by Jim Morrison and The Doors. Which I believe came out in 1968, but you can fact-check me on that if you want.
That is common of Doors cover bands to do which is to use the name of one of The Doors songs as the name of their band. There's a band called Peace Frog. Another band called Strange Days. Have yet to see or hear of a band called Light My Fire or The End, or Roadhouse Blues, but they may exist as well.
I mean not every Doors cover band could call themselves The Doors, for obvious reasons. Or Jim Morrison and The Doors, again for obvious reasons. Because you would have a hard time extinguishing from one to another. Or even, "this is The Doors Cover Band" as someone is introducing them. The way to tell each of these bands apart is by their name of course, but also accuracy. Who looks, sounds, and plays the part the best, or even does a good job.