One of my characters is originally known by his nickname (only for introduction) then known as AJ. Would I write that in my final publishable draft as AJ or A.J. ?? No one ever uses any other name....just the initials A.J. Examples: TJ Smith instead of "Terrance John" JB Walton instead of "John-Boy" AJ Stapleton instead of "Andrew James" "Hi TJ, how are you doing today?" Frank asked.....versus......."Hi T.J., how are you doing today?" Frank asked. Which way is correct - with or without the period after the initials?
I would say no periods for nicknames, yes for formal abbreviations such as in a letterhead or if you are describing a business card. But the only thing that matters is being consistent. You might also consider a space between the letters. JR might be clear because the R is capitalized, but J R is clearly not pronounced Junior.
Hate to go against the grain, but I once got feedback on a manuscript from a professional editor on this very issue, and she said periods with a space between the letters. So "A. J."