You know that the full name of the Gallic emperor was Gaius Pius Esuvius Tetricus. Gaius was his personal name, and either Esuvius or Tetricus was his Nomen or clan name. If Esuvius was his Nomen or clan name Tetricus would have been his cognomen, the name of his family within his clan. The son and caesar and possibly co emperor of Tetricus was also named Gaius Pius Esuvius Tetricus though usually known as Tetricus II in English.
If Tetricus was a cognomen, it is important to note thatCognomen were hereditary and passed on from one generation to the next, and that many cognomen have obscure and uncertain meanings and it was common for a cognomen to be based on a nickname. So if the meanings of Tetricus include cheerless or dark, the original Tetricus ancestor would have been nicknamed Tetricus because he was either gloomy or cheerful, depending on if the nicknamed was meant literally or ironically.
Considering the scant available information about 3rd century Roman history I doubt that there is a recorded anecdote about why the ancestor of the Gallic emperor was named Tetricus.