Japanese Translation. . .?

And please don't insult my intelligence and tell me to go to Google Translate. That doesn't work, I know for a fact. Basically, in a story I'm writing, there is an island in which the locals believe dragons live. I want to give it a Japanese name that means something along the lines of 'land belonging to the dragons' or 'dragon's island'. I don't understand enough about the Japanese language to know exactly how the grammar and such works, so I'll leave it to you to give me as close a translation as you can. If what you give me is a variant of what I want, that's fine. I just want authenticity. Thank you very much for taking the time to read my question and a special thank you to those who answer it.