Jr., Sr., III
The terms Jr., Sr., III and the like used after a person’s name are part of the name and thus generally do not take a comma:
Lonnie Poole Jr. gave a generous gift to the university.
If a person requests that we use the comma with his or her name, we should grant the request out of respect for the individual. We should also remember that when a building, fund or other entity is named after a person, the entity and the person are distinct from one another, and so are their names. Hence, at the request of Gov. Jim Hunt, we use the comma in his name.
Gov. James B. Hunt, Jr. spoke to an appreciative audience.
But there is no comma used in the full name of the Hunt Library:
The James B. Hunt Jr. Library is one of the most technologically advanced learning and collaboration spaces in the world.