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Not really the place to ask this, as it's a general modding question, not specific to Lux Invicta.

Nicknames are defined in common/nicknames/. The actual text of the nickname goes in a .csv file in localisation/, in the same format as any other localization.

If you have something like:
Code:
nick_the_conqueror = {}
it is gained only by event (or in history, as the result of a war won or lost, or in the effect of a decision)

If you have something like:
Code:
nick_the_lisp_and_lame = {
   allow = {
     age = 16
     trait = lisp
     trait = clubfooted
   }
   chance = {
     factor = 5
   }
}
the nickname can be gained at random if the allow conditions are met (age 16 or older, and having the traits lisp and clubfooted) with a 5% chance of happening.

Look through the nicknames files. If anything confuses you you can ask again.