They should change their name to Lakota Fanning.
The Dead Kenny G’s
I can’t think of anything more fitting than a-ha with only three letters and all lower-case.
(Edit: oh, you’re not actually looking for puny band names.)
Not a punny name, but that sounds like why Ace of Base is named that rather than Ace of Bass, which would cause some to pronounce the last word like the fish despite the rhyming clue of Ace.
They need a tribute band called Ass of Bass.
After leaving Soft Machine, Robert Wyatt formed Matching Mole, based on the French translation of “Soft Machine”: Machine Molé.
LOL! A stealth threadwinner, that.
How about The Beat Farmers?
Which makes me think of the fictional band in High Fidelity:
Kathleen Turner Overdrive
I once did hear of an indy novelty band called Petty Cash – they did Tom Petty and Johnny Cash covers, of course.
But, for an actual serious band with a somewhat punny name, I nominate the 1970s rock band Sniff ‘n’ the Tears.
They may have been only regional:
Phil ‘n’ The Blanks
Definitely local but I saw a band many years ago which consisted of rather elderly gents performing Bob Dylan songs under the name of “The Zimmer Men”.
Central Coast California has an elderly surf band called The Dentures.
Ha!
In such a thread, I’d offer “The The.”
…or X.
Does The Pretty Reckless qualify as punny? The lead singer is Cindy Loo Who from Jim Carey’s The Grinch.
How about a self-prophetic name
Flash 'n the Pan was a one-hit wonder.
Not a pun, but Death Cab For Cutie was named after a quirky song (an Elvis pastiche) by The Bonzo Dog Doo-Dah Band.
I have no idea what their music is like, but I saw an album of theirs in a record store decades ago, and it’s been my favorite band name ever since.
There is also Sultans of Ping, a pun on the Dire Straits song.