"Tree swing" seems fine to me (native speaker as well), the commonality of all pictures is it is a swing, set up in a tree (albeit incorrectly or poorly in many cases). If I google "tree swing" it is clear that this is not a particularly rare way to refer to this specific sort of swing.
Yeah, it's worth noting that "tree swing" isn't a common idiom; I only meant a swing that's set up on a tree. I just didn't want to call it a "tire swing" though because it only took that form in one panel. Maybe "rope swing" would be the best name for it?