I haven’t gotten a chance to watch the series yet, but I got some suggestions that might help you. I’m sure there are plenty of islands that have been inspired by it. Try googling it! Pinterest is a good place to look for design ideas
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For name ideas, you could name it after a location in the anime or if it is set in a different world, name it whatever the world is called? That is probably a better idea if you plan on decorating the island based on multiple locations and not just one.
What I do when I’m decorating, is try out the furniture at harv’s studio and a small setup to figure out what I may want to do with my island. I order the items when I figure out what items I think would work with the theme. I’m working on a second island, which is based off a favorite game and I’ve been figuring things out through Harv’s studio, some photo editing projects too that I’m doing for my island journal. A big help had been finding a dream address based on the same game; that is what led to my decision to try making my own. I’m not anywhere close to being ready to decorate, but I’m brainstorming and it is helping give me a more clear idea what I want to do.
If you had a more solid idea of what you were thinking, I could probably help you more in spite not having watched it.
Do you have an ideas what villagers that you want to have? Color scheme?
What about Demon Slayer in particular inspires you? (If everyone, maybe specify some of your favorite things so some of us can help you better)
If the anime takes place in Japan or a setting like Japan, consider bamboo items and growing bamboo.