I just used my name again for the nickname the first time I played. It was kind of weird in some instances. They tried portraying Trevor as a character who felt it was "too soon" to start referring to someone by a nickname, and there was at least one instance of him saying "Hey, [Name]-- Uh, I mean, [Nickname]," which definitely sounds weird if you used the same name for your nickname. As cute of a feature as it is, I think it definitely works better in Japanese, where people will refer to others with differing honorifics depending on how close they are, and may even shorten their name when doing so.