Dr. ‹First Name›: a good nickname or a "professional cancer"?
Going by "Dr. FirstName" is just confusing. If people aren't familiar with you, they will think it is your last name. If they do know you, it doesn't seem more casual, just odd.

It depends on the context and culture, but in the US it is standard to go by either "Dr. LastName" or just "FirstName." Like Solar Mike mentioned, a shortened form like "Dr. Initial" is sometimes used for students to refer to you.