There are far too many to name here. The Chicago White Sox franchise has existed for more than 100 years. They are one of the Original 8 teams that formed the American League.
To name a few: "Shoeless" Joe Jackson
Eddie Collins
Ed Walsh
Ted Lyons
Ray Schalk
Red Faber
Luke Appling
Harry Hooper
Early Wynn
Luis Aparicio
Hoyt Wilhelm
Nellie Fox
George Davis
Carlton Fisk
Tom Seaver
Frank Thomas
Robin Ventura
Bo Jackson
George Bell
Michael Jordan (minor leagues)
Mark Buehrle
A.J. Pierzynski
Magglio Ordonez
Bobby Jenks
Paul Konerko
Jim Thome
Jermaine Dye
The list goes on and on...(almost all of these names are in the Hall of Fame)
Non-players include:
Harry Caray (broadcaster) famous on the South Side of Chicago as White Sox announcer long before he joined the Chicago Cubs.
Alejandro De Aza is number 30 on the Chicago White Sox.
The Chicago cubs and Chicago white sox
Gordon Beckham is number 15 on the Chicago White Sox.
In 2006, the Chicago White Sox had a 90-72 record.
Leury Garcia is number 28 on the Chicago White Sox.
In 2008, the Chicago White Sox had an 89-74 record.
Adam Dunn is number 44 on the Chicago White Sox.
Adam Eaton is number 1 on the Chicago White Sox.
Adrian Nieto is number 17 on the Chicago White Sox.
Alexei Ramirez is number 10 on the Chicago White Sox.
Andre Rienzo is number 64 on the Chicago White Sox.
Charlie Leesman is number 61 on the Chicago White Sox.