Thrifty Car Rental
Thrifty Car Rental operates from the rental car counters at Key West International Airport, a few minutes on foot from the terminal. It is one of the Hertz family of brands, alongside Dollar and Hertz itself, so the counters and the lot are shared with its siblings.
The question of whether to rent at all is worth thinking about before you book. Key West is four square miles, flat, and built for walking and bicycles, and parking in Old Town is the single most common complaint visitors have. If your week is Duval Street, Mallory Square and the beach, a car will mostly sit there. If you want the rest of the chain, a car is the only way to get it: the Seven Mile Bridge at golden hour, Bahia Honda State Park, the Blue Hole on Big Pine, the roadside places in Marathon and Islamorada, and the drive itself, which is the attraction as much as anything at either end of it.
Confirm counter hours before you book a late arrival or an early flight out. This is a small airport and the counters are not staffed around the clock, whatever the booking aggregators say.