Question

Does Hi Cory need a new punctuation

Answer 1

In my opinion, I would have said "Hi Cory!" But, if not you should just keep it simple and write "Hi Cory."

Answer 2

To sound more sophisticated it could be written as: Hello, Cory
To add punctuation it would be simply: Hi, Cory
Or if casually like if you were texting it could be: Hi Core- left the same.