Never seen anything published that explains why in 1968 they dropped the "The" from The Rolling Stones for the album cover.

Most of the singles say The Rolling Stones except from 1991 onward.

Even EPs and 12" singles varied. The 12" singles from UNDERCOVER, an album labeled Rolling Stones, say The Rolling Stones on the spine but Rolling Stones on the cover.

LPs album covers titled as The Rolling Stones:
12X5
Now
Out Of Our Heads
December's Children
Big Hits 1
Between The Buttons
Get Yer Ya-Ya's Out
Sticky Fingers
Goats Head Soup
Black And Blue
Love You Live
Some Girls
Time Waits For No One
Emotional Rescue
Sucking In The Seventies - some
Rewind
Jump Back
Rock'N'Roll Circus
Stripped
Bridges To Babylon
A Bigger Bang
2012 hits

All others are Rolling Stones except these with no band name:
The Rolling Stones
Aftermath - only the title
Flowers
Their Satanic Majesties Request
IORR
Blue And Lonesome

I’ve often wondered about this myself. Never have saw a reason listed anywhere and just figured maybe it was artistic choice at times for some of the album styles, but honestly have no idea.