Rare Earths name came from 1968.
LBM is a true example from 1964, (It had an articled name apparently before) but it’s another culture, language, and continent. There’s that.
Too late (1974) and does not conform. It’s a family name (even though it was made up) and even though sometimes styled as Ramones, usually seen as The Ramones.
No; his is a possessive pronoun. In English there are only three articles: *the *(definite), and a and an (indefinite).
Hm. To me the article is implied I suppose. It doesn’t fit the way I understand the OP. “His” stands right in the place of “The” and is a substitute for it. Most popular references were to “The Comets” IIRC, at least I have never heard of “Bill Haley and Comets.”
Chuck Berry records were sometimes credited to CB “and his combo.”
Ramones shows famously began with the phrase “WE ARE THE RAMONES!”
I’m not debating whether if fits the OP, just stating the grammatical facts.
Mountain (69)
Jethro Tull (and predecessor band McGregor’s Engine, 67)
Creedence CR (67)
Moby Grape, Buffalo Springfield (66)
Big Brother and The Holding Company (65)
Canned Heat (65)
That then brings up Scorpions. Everybody *says *“The” Scorpions, but it’s actually just “Scorpions”, no “the”.
Formed 1965 (though their first album wasn’t until 1972).
I thought it might be Golden Earring, 1961. But researching it, I see the started as The Golden Earrings, dropping “The” in 1967 and the S in 1969.
Is the question limited to rock bands? Is it limited to ones from English-speaking countries? I am sure there are plenty of non-English bands that don’t use the English “the” in their names, and there may even be some that don’t use a local word that is more or less equivalent to “the”. Even the Soviet Union had rock bands in the early 1960s, and many of the languages spoken there (most notably Russian) don’t even have articles, definite or otherwise.
Also Jethro Tull are a name, like Alice Cooper
Thanks, everyone – I was offline all weekend and I can’t believe how much debate this silly question generated! Based on first released recordings, the winners (sa far) seem to be:
International:
[ul]
[li]Ladysmith Black Mambazo (64)[/li][li]Them (64)[/li][/ul]
US: Canned Heat (65)
I was wondering when someone would bring them up!
(Not Them, just them.)
Downliners Sect also had their first releases (an LP, and EP, and a single) in 1964.
There’s also the similarly named Blues Incorporated, whose first single was (I think) released in 1959. They were never really popular as a band, but were influential on rock musicians.
I thought I was the only one who knew this. 
I always call them, *“The Pink Floyd” *just to be a dick.
I had never heard this. Interesting.
With bands that are in my frame of reference, it seems like 1965 was the year the name improvising really took off thanks in no small part to the psychedelic scene. To add a couple more, Love (Arthur Lee’s band) and Quicksilver Messenger Service also formed in '65.
Herman’s Hermits is an interesting example, as I think of that as pretty calculated, formulaic music. When I was a kid and would hear their name, I could never make it out. It sounded like a fragment of a tongue twister. Apparently the origin of the name briefly was Herman & His Hermits - technically that counts too?
“Girls of the Golden West” was a country group formed in 1933. They were fairly popular in the 30’s and 40’s.
If you look they don’t really qualify. They are even more connected to their article than the ramones or the MC5. Look at the title of the debut LP.
Although I do have a feeling that getting pedantic and detailed using wikipedia may not lead to Truth.
Love is a great example that I forgot. They were the most pain in the ass of them all because you always had to say “Arthur Lee and…” so that you wouldn’t have to repeat stuff while people didn’t grok it.