One could probably write a thesis on the rise, fall, and resurrection of the definite article as part of band names. In the early days of rock, the “the” was standard. Dropping the definite article seemed to become a thing in the late 60s psychedelic era, and reached its height in the early 70s, especially with progressive rock bands - hence you had names like Jefferson Airplane, Traffic, Cream, Love, Yes, Pink Floyd. With the advent of punk and New Wave, there was a resurgence of the “the”; we got The Sex Pistols, The Buzzcocks, The Clash, The Cars, the Police etc. - and of course The The. I would suggest that at least some of this was intentional, trying to signify a break with what they perceived as the pomposity of the music of the recent past.
I can never remember whether it’s “The Psychedelic Furs” or just " Psychedelic Furs".