This is the most likely scenario. Many merry-go-rounds feature various animals or objects as seats, and aeroplanes could be one of them. These could be realistic airplanes or take a more whimsical approach with cartoonish features.
This is less common, but there could be a ride that combines some elements of both aeroplanes and a merry-go-round. It might have a circular platform with individual aeroplane-shaped cabins that spin independently or together.
There isn’t a single, universal name. They might be called “aeroplane carousel,” “flying animals carousel,” or something similar depending on the park.
Imagine a classic merry-go-round with some of the painted animals replaced by aeroplanes. These aeroplanes could be realistic models or have a more cartoonish style.