Every public facing, serious API I've worked on has had users trying to game for free usage. You have to build systems to prevent it. The user OP describes sounds more like what you point out, rather than running multiple accounts.
OP, can you reach out to them and ask why? Ask them what they like about it and what they are using it for first. Try to work with them rather than against. Maybe offer them a 6 month deal, maybe the call is enough
