The history lesson it gives going back to the 1890's is illuminating, but me being me, I'm most interested in the bands I listen to, most of which have flourished since the beginning of the '60's.
In thinking about music going back that far, it seems to me that the use of the definite article was the more usual one. The Beatles named themselves in deference to The Crickets, who themselves had taken inspiration for their name from the doo-wop groups of the '40's and '50's, who were almost invariably had names of the form /The [songbird]s/.
The Rolling Stones and The Who and The Kinks and The Beach Boys and The Ventures and The Turtles and The Monkees and The Zombies and The incredible motherfucking Sonics and The Kingsmen and The Trashmen and The Shadows of Knight and The Mindbenders and The Count Five and even The Beau Brummels.
American bands to pick up on the trend started by Messrs. Marriott and Jones and Lane and Mclagan were led it seems by San Franciscans. Quicksilver Messenger Service and Jefferson Airplane come rapidly to my mind. A more detailed search of Billboard's Top 100 by year shows that "Somebody to Love," released as a single in April of 1967 makes Jefferson Airplane the first band in Billboard's Top 100 to skip the The.
"A Whiter Shade of Pale" from May of the same year makes Procol Harum the second. Small Faces could have been third, right? In 1968, Billboard's list would include Cream, Steppenwolf, 1910 Fruitgum Company, Blue Cheer, and Vanilla Fudge.
So, raise your consciousness and drop the definite article, everyone.
But consciousness-raising is hard, I guess. It's worth noting that Jefferson Airplane and Cream, although they were never credited on a record with the definite article, were often credited on posters and gig flyers that way.
Status Quo made Billboard's list for "Pictures of Matchstick Men" of course, and when they did so, they went by their name with the definite article attached. In 1969, they decided that they wanted to drop it, so you can date your copy by whether or not "The" appears on the sleeve or the label.
A little similarly with Pink Floyd. Syd Barrett originally named them "The Pink Floyd Sound" which got shortened to "The Pink Floyd" before they signed and then was further chopped to "Pink Floyd" after the release of their first single, "Arnold Layne."