ELO Electric Light Orchestra
Mentioned in the OP.
A couple of others, gleaned from songs on my iPhone:
O.A.R. (short for “Of A Revolution”)
REO Speedwagon (name taken from an early truck model; REO were the initials of Ransom Eli Olds)
But what do those letters and number mean? Hmmm? 
The Average White Band were often known as the AWB and used that for an album title.
Apparently the James Brown’s backing band (themselves known as the JBs) recorded a track in tribute to an AWB song and gave themselves the credit AABB for Above Average Black Band.
TCMF-2L
**MxPx **
“MxPx began in July 1992 with the name Magnified Plaid. Initially, the band started playing music inspired by Descendents, Black Flag and other punk rock bands. Mike Herrera, Yuri Ruley, and Andy Husted were classmates at Central Kitsap High School in Silverdale, Washington and were 15 years old when they formed the band. The name was a tribute to the original guitarist’s fascination with plaid shirts but did not fit on the band’s posters. Consequently, the name was abbreviated to M.P. But in Yuri Ruley’s handwriting, periods appeared as Xs, and since he made up the show posters for the band, the four-letter moniker stuck.”
NOFX
“In 1983, guitarist Eric Melvin met bassist/vocalist Mike Burkett (Fat Mike) and started the band under the name NO-FX, after a Boston hardcore punk band called Negative FX.”
SNMNMNM
“The group’s name is a condensation of “Seamus 'n Matt 'n Mark 'n Matt”.”
It’s a secret.
TCMF-2L
(But they are not random.)
TSO - Trans-Siberian Orchestra
BOC - Blue Oyster Cult
American R&B girl group TLC.
TCMF-2L
Y&T (Yesterday and Today)
Andy Partridge has said that, when naming the band, “XTC” was seen as a “shorthand way of writing ‘ecstasy’” (cite). There’s probably some gray area between it being an acronym and an initialism.
One final post.
The GTOs or Girls Together Outrageously were a girl group associated with Frank Zappa.
There was an Australian band called WTO (World Trash Orchestra) who became GTO (Global Trash Orchestra.)
For good measure there have also been at least two songs called GTO.
TCMF-2L
Does PDQ Bach work?
Were they even a band?
Am I really that lazy?
The very Australian TISM.
Both of these only use the acronym/initialism normally:
AFI - A Fire Inside
T.S.O.L. - True Sounds of Liberty
Atari Teenage Riot is sometimes ATR.
One hit wonder MARRS
M.I.A.
Flat-earther B.o.B.
Murs
The D.O.C.
N.E.R.D.
"It’s BTO. They’re Canada’s answer to ELP. Their big hit was TCB. That’s how we talked in the '70s. We didn’t have a moment to spare. "
-Homer Simpson. In a later episode he heckles them to "play no new crap, and skip to the “Working Overtime” chorus.
Urban legend, isn’t it?
You forgot S.O.D. side project (so side project of a side project), M.O.D. Respectively, Stormtroopers of Death and Method of Destruction.
Whose biggest hit was TSOP.
U.K. ( a British progressive rock supergroup originally active from 1977 until 1980).
Here’s an Indian band called XLNC. I have no idea what Mere Yaar Ne means but I love this song.
Oh, and apparently TLC doesn’t stand for Tender Loving Care but for Tionne"T-Boz" Watkins, Lisa “Left Eye” Lopes and Rozonda “Chilli” Thomas. I learned something new today!
MC5 – short for “Motor City Five”