Is it allowed for an individual to register and use two separate Google Accounts? I know it's possible seeing that the same phone number can sometimes be used to register a new account, but is it allowed? I am consider doing this for organizational purposes but am wondering would I get banned?
It is certainly possible - I have multiple. I have not found any mention of Google limiting the number of accounts you can create, in fact, Google's documentation mentions ways to sign in to multiple accounts at once.
But if you're doing this for "organizational purposes", there are probably better ways to achieve your goal. Using multiple accounts will require some changes to how you are using your browser, for example. You cannot easily browse two Gmail inboxes in the same browser window.
AFAIK, it's allowed that an individual register multiple accounts for personal use, not for "organizational purposes". Please read the Google TOS.
It's worth to say that there are reports of limits of the number of accounts that could be created using the same phone number that is not publicly disclosed in order to prevent abuses. I saw this reports on several Google Product Help Forums
For the massive creation of accounts for "organizational purposes" there is G Suite.