I used Avis on a recent Iceland trip. Note that Akureyri is a relatively remote place; this is not like landing at Frankfurt and waiting for a recent return to be turned-around and issued to you. Apparently, there is WIDE variation in a VAST number of local rental companies in Iceland.
It is also the case that not only is everything very expensive in Iceland, car damage events are frequent, multiple kinds (like "Wind and Stone Coverage") of insurance are generally wise to buy, and driving conditions often difficult for US Interstate and Mall Parking Lot drivers. Your car windows will have a sticker, "Open door with BOTH hands fully gripping the door. Wind can rip off the entire door."
I was glad that Avis gave me a complimentary upgrade to an automatic and a crossover-SUV with 2-wheel drive. (July trip. Manly-AWD completely unecessary for 95% of all visitors then.) We needed the ground clearance, and the driving was, simply ... ENDLESS. Edit: You didn't give your month of travel, but I'll mention that in winter, the Iceland Rescue Societies have an expression, "Death By GPS." We used Waze, which was fine, in good weather. Their phrase refers to blind faith and obedience to ... the computer. Non-fatal example, Waze wanted to cut 1000' off a paved crossroads left turn by using a diagonal that was ... unpaved. Besides, the left turn is safer at a place that has, at least, two Stop signs. (I know, stop signs are for losers.)
https://community.ricksteves.com/travel-forum/trip-reports/western-iceland-by-car-summer-2023
ImaFarmer: I try to book hotels and cars and air tickets directly with the actual provider. The improved access and control of the rental is worth any swaggering illusion of bargain-hunting with a consolidator like Booking or Expedia. I don't want to have to deal with a third party if I have a delay or cancellation, and I want to be treated as the actual customer.
I'm quoting my own TR here, but it bears repeating:
"The big roads are barely two lanes wide. Typical speed limits 90 KMH rural, 70 and then 50 approaching towns, 30KMH in town. I hugged the side white line when a bus or truck passed the other way. On the unpaved roads, they were usually so narrow that you had to slow down for opposing traffic."
I observe in northern New Jersey that most Americans have no idea where the perimeter of their Chevy Suburban or Lexus is, and they are not inclined to pull to the right even when they see a parked Amazon van partly blocking the opposing lane of traffic. What Me Worry? Is it any wonder there are so many accidents in Iceland?