mine is Mosspath!
Hollow Knight was a huge influence. How locations are named in that game fits the supporting environment so well...I want my island to be filled with plants, so I wanted it to sound like how I want my island to look. I think it sounds pretty cozy too.
I will only get my game on Monday, but I'm 99% sure I'll name it Paon. I'm planning on going for a jungle theme like the Faron region from breath of the wild and to me that name sounds fitting.
I named mine Eressea, inspired by Tolkein's Tol Eressëa!
"Tol Eressëa (Q, pron. [tol eˈresːe.a]) was a large island off the coast of Eldamar. Its name translates from Quenya as the Lonely Island, for it lay originally in the middle of the Belegaer, far from any other landmasses."
I called mine High Roost. If the Roost does come to New Horizons (no spoilers please), then it'll feel like a natural part of the town. When I start up the game I to think to myself "Hi(gh) Roost" and when I quit I think "Bye Roost", which is silly, cute and in keeping with Animal Crossing's puns. In my mind residents of High Roost are called Roostlings.
I'm not sure where the inspiration came from, I think I was looking up names of animal homes. I was also trying to think of a name that incorporated the verticality I'm planning for my island, and felt on brand for Animal Crossing from a worldbuilding perspective. The name also reminds me of LoZ Windwaker, which is one of my favourite games.
I named mine "Ydalir". It's a location in Norse mythology. Supposedly not all that significant, but I liked the sound of the name. Another contender was "Breidablik", also Norse.
I always like to use names from various myths if I can't think of anything else.