Anyone know the name of this business?

You might be referring to Fant-a-Sea Rentals, which moved out of that location, but probably still have a place in Destin. Now, a kayak and bicycle rental business, Butterfly Rentals (with main store in Seagrove), has moved into that location.

Thank you SJ for the information, I know our renters may be disappointed, but I can't quite say that I am devastated that this particular line of business is no longer on 30-A. ;-) Nothing against Fanta-Sea, of course, just maybe against crazy tourists on scooters. Or from what I've read, crazy locals, too.
But at least I did my bit by asking!

I say no scooters in the hands of beginners on our roads! They are just dangerous. I have no problem with experienced scooter operators, but I do have a problem with people expecting them to be easy to operate if they have never been on one, and havent ridden a bicycle in a while.

They are all over Key West where I just moved from. Nightmare.
Noisy ( yes we get it you are on vacay now lay off the horn)
Pollutants (why no electric ones)
Finally, the local paper stopped putting in the EMS reports due to all the accidents.
Flip flops are not an ankle protector when you clunk the curb

so me too, no 30a scooters please