This part is fine. It was recently discussed in a similar thread where a parent wanted to set up a new Bnet account for their son instead of having them play on the parent account.
If he has characters on your account and you want to allow him to keep playing them, you’ll need to use the Character Transfer service. You should be able to gift him Character Transfer Tokens through the shop (they are currently on sale right now).
He’ll need one for each character he wants to transfer, so depending on how many that is, it might get expensive.
Assuming you share the same last name, and that is what he used to set up his Battle.net account, transferring characters from your WoW license to his should be easy enough. As Vorsol noted though, any Battle.net account bound item like mounts, heirlooms, appearances, toys, etc… will not transfer with the character so they will have to earn their own collection on their account.
If the names do not match, we may still be able to help but you’ll need to submit a Support ticket
You should only have been playing on the account of your parent though, not on your you uncle’s account. People can not give you characters.
That said, the transfer restrictions are listed here