That's a good question! If the website you created is the only one in your account, you can simple just update the account and credit card information to match the new person taking over. You can manage this by going to Account > Contact Info & Security and Account > Billing & Payments.
If you have several websites in that account, you would have to have the organization create a new account. Once you've done this, you can transfer an existing site by going to Websites Manager > More > Import Page to your account