Fame isn't necessarily measurable is it? How would you pick one person and say they are the most famous, or more famous than someone who is apparently equally successful? I'd guess the one figure that would be the most immediately recognizable to the largest group of people would probably be Dwight Eisenhower.
Here is another one-Alf Landon the Republican nominee for President who ran against FDR. He was the father of Nancy Kassabaum Kansas Senator who also served in the US Senate.
Jack Kilby (inventor of the microchip, nobel prize recipient)
R. Lee Ermey
Robert Gates
Barry Sanders
Joe Walsh
Melissa Etheridge
the Carney brothers (founders of pizza hut)
Kirstie Alley
the Koch brothers
Russell Stover
Ed Asner
Amelia Earhart
George Washington Carver
James Naismith
Since Dwight Eisenhower was born in Texas he wasn't a true Kansan but some others to add to the list:
Roscoe Fatty Arbuckle
Clarence D. Batchelor
Gwendolyn Brooks
Walter P. Chrysler
Clark M. Clifford
John Steuart Curry
Bob Dole
Milton S. Eisenhower
Carl A. Hatch
Dennis Hopper
Walter Johnson
Buster Keaton
Emmett Kelly
Stan Kenton
Harold Lloyd
Edgar Lee Masters
Hattie McDaniel
William C. Menninger
Gordon Parks
Zasu Pitts
Charles Buddy Rogers
Damon Runyon
Eugene W. Smith
William E. Stafford
John Cameron Swayze
Vivan Vance
William Allen White
Charles E. Whittaker