Scholarship Qualifications
Collegiate wrestling is a lot like professional wrestling in this case. No, you don't need a nickname or a gimmick—go nuts if you want; just don't tell your coach—but you need titles. Belts, if you will.
Imagine each requirement as a ladder. You need all the stuff for Division I that you do for Division III, but there's more. So let's start at the bottom. And remember, these are only guidelines if you want to have any hope of getting some scholarship money. These aren't guarantees.
For Division III, you need to be All-League or All-District, and you need to have multiple tournament wins. For Division II, you need to be All-State. For Division I, it's All-American, All-Region, and presumably All-Planet if aliens ever invade.
And as a reminder, wrestling is an "equivalency sport," so the chances of getting a full ride are basically zero (source).