While the name of Tommy Thomas is certainly alliterative, it is also owned by a very good Pitcher. 

Frank Smith debuted as a Rule 5 Draft Pick in 1904, and he paid immediate dividends in his first two seasons with 35 Wins and with both of his seasons seeing him secure top ten finished in ERA.  It was a good start, but there was a valley before he would hit the mountain.

A superstar in Cuba, Jose Abreu defected in 2013, and it was the White Sox who won the sweepstakes to sign him.

Johnny Mostil would play all 972 of his Major League Games with the Chicago White Sox, and for a brief time, he was considered one of the quickest players in the game.