The answer is no, you do not use a comma before "II" or "III" in a name.
Here's why:
* II and III are part of the name: They distinguish the individual from other people with the same name.
* Commas separate parts of a sentence: In a name like "John Doe II," the entire phrase is considered a single element.
Example:
Correct: John Doe II
Incorrect: John Doe, II