Each title that follows a name is set off by commas.

Incorrect: Kenneth Griffey Jr. could have broken Maris’ record.
Correct: Kenneth Griffey, Jr., could have broken Maris’ record.

Correct, if pompous: The book was written by John Kenneth Galbraith, A.B., M.A., Ph.D., D.Sc., Litt.D.
(Note that each title is set off by commas.)

Numerical titles following a name are not set off by commas.

Incorrect: Aloysius Otto Culp, III, is better known as “Buzz.”
Correct: Aloysius Otto Culp III is better known as “Buzz.”