Are there only specific kanji that can be used to create names? I decided on names for some of my personal characters a long time ago, and now I'm trying to figure out what kanji can be used to spell those names. How exactly does creating a name in Japanese work?
There is an official list of government approved kanji that can be used in personal names. It includes all the kanji you’d typically encounter on renshuu plus a few more. Search for nanori (名乗り) or jinmeiyō kanji (人名用漢字).
The official list is enforced by the koseki (戸籍). The local government office will not allow changes to the family register that use non-jinmeiyō kanji.
I think the easiest way to search for kanji for your OCs is to use a site that allows you to search by kana. I like Jisho.org, but kanshudo.com has the same feature, as do any number of Japanese sites aimed at parents looking to name their babies.