If you're worrying about the TOS, you're free to check it.
COINBASE USER AGREEMENT2.1. Registration of Coinbase Account. In order to use any of the Coinbase Services, you must first register by providing your name, an e-mail address, password, and affirming your acceptance of this Agreement. Coinbase may, in our sole discretion, refuse to allow you to establish a Coinbase Account, or
limit the number of Coinbase Accounts that a single user may establish and maintain at any time.
If I understand it correctly, the bolded phrase means that a single user could have more than one account, it's just that Coinbase will decide if how many you could maintain.
COINBASE PRIVACY POLICYIf you close your Coinbase account, we will mark your account in our database as "Closed," but will keep your account information in our database for a period of time described above. This is necessary in order to deter fraud, by ensuring that persons who try to commit fraud will not be able to avoid detection simply by closing their account and opening a new account. However, if you close your account, your personally identifiable information will not be used by us for any further purposes, nor sold or shared with third parties, except as necessary to prevent fraud and assist law enforcement, as required by law, or in accordance with this Privacy Policy.
This one is about closing an account. However, the difference is that Coinbase will be the one to close yours and not you directly. That being said, they won't think that you plan to commit fraud, especially their rep advised you to do that. Just keep your proof of conversation with their rep just like what others have mentioned for future use in case they asked you.
EDIT: Same issue as you on this
reddit thread, and it ended up solved
Don’t give up! They resolved my issue after a few days of creating the new account.