Just searched through my Twitter for band names I’ve stumbled upon.
Accidental Eyebrow
Spontaneous Sister
Farting Sheep
Butt Snorkels
The Benedict Cumberbatch Rhythm
Peculiar Car Gnome
I think a band name should be appropriate for the music style they play. I’m sure I’ve misjudged a lot of bands because of some stupid name that makes me think of unpleasant music.
Oh - and in case anyone is curious, we’re probably going with The Dropped Note String Band. Google shows no conflicts. I’m sure you’ll never hear of us! 
Sort of a joke, as dropped notes are the notes you don’t play in a complicated piece. Wasn’t anywhere among my top choices, but when we started trying to reach consensus, there were only about 5 names that as many as 3 of the 5 kinda/really liked. And The Dropped Notes was the only one that 4/5 kinda and really liked. I didn’t absolutely hate it, so I went along. One other guy suggested adding String Band.
An interesting exercise.
Well, there’s your band name. What’s your banjo players name? Say it’s Gary. Call your band “Missing Gary”.
I’ve struggled with band names on plenty of occasions. Keep searching- there’s one out there for you.
ETA: Oh! You got one! Good name!
Obligatory Spinal Tap link:
https://www.youtube.com/watch?v=PROS7aKoZuY
By the way, I see the name “The New Originals” is taken.
Well, I made up a band name that seemed appropriate and that I was pretty sure wouldn’t have already been used. And yet…the Down Homers is indeed a country band.
Just saw and fell in love with “Billy the Squid and the Sea Cow Drifters”. Awesome. Check ‘me out.
The Wishing Wells
Ponds and Guppies
Barb Wire and Fence Posts
Tower of Hay
Pebbles and Creek
A guy who went to my college a few years before me was in a band called The Young Johnny Carson Story. I guess they eventually got around to asking Carson for permission to use his name. His lawyers said no and told the band they’d sue if the band didn’t change the name immediately. Oops!
If you don’t mind an unsolicited thought, consider going with The Drop Note String Band (or The Drop Notes), instead of Dropped. It rolls off the tongue more easily, and your fans can shout it. It’s not grammatical, but that will help with trademark issues once you hit it big. 
I’m not seeing evidence of this, so I guess it’s still available.
When I was a tween, a friend and I decided that if we ever started a band, we would call it Magnum Progression, complete with a logo (in rippling rainbow colors, BTW - this was, after all, the late 1970s). I just Googled that phrase and came up with this.
p.s. Upon Googling “Slow Motion Ramblers”, the fourth link was to this thread.
Hell - love the input. I think our initial agreement was on Dropped Notes - but I thought the sibilant S preceding String Band made it difficult. So we discussed all of the variants: Dropped Notes; Dropped Note; Drop Note; Dropnote - not to mention String Band vs Stringband.
I think the consensus is Dropped Note String Band. For me, a dropped note means something, as opposed to just dropnote, and string band is the accepted description of our type of instrumentation. But I’m more happy to get consensus on something than I am on the specifics.
I’m sure the old folks will be hollering out our name a week from Sunday. Hope no one uses their lighters to call for an encore, as I’m pretty sure a few folks are on O2! 
BTW - if I google now, this thread comes up. So take that as notice all you mando/banjo/fiddle/cello/tenor guitar/bass combos out there, and don’t go stealing our name! 
Incredible. I was going to suggest ‘Tri State Killing Spree’ but a quick google reveals the name has already been taken. The name just popped into my head, but I guess I must have heard it before someplace. Huh.
Ben Day and the Dots.