It would be hard for him to remember his name after changing it several hundred times...esp. if questioned suddenly by the police or anyone else for that matter...a minor detail for the show but in reality...hard. Think about it! (Damn- What name did I just give?) It would take a lot of concentration...Steve
Well actually there were about 109 aliases Richard Kimble used throughout the run of this series. Of course those are the ones we know about - there could have been more (and undoubtedly were.)
Being a doctor of medicine he would have been a man of higher intelligence and would have been mentally sharper than the average Joe.
In real life David Janssen had a photographic memory. He (like other actors such as Mickey Rooney and Robert Mitchum) could read a script through one time and have it memorized.
So it's not too hard to imagine Kimble being able to pull off this feat. Of course with the stress and pressure he was often under (as you mentioned) it would have made it more difficult, but he usually stayed in one place for a period of time. That would give him time to settle into his new idenity.
There was actually one episode (sorry, I don't remember which one) in which Kimble actually is so beaten down by the stress of his situation that he inadvertantly signs in to work under his real name, rather than his current alias. As I recall, that occurred at the beginning of the episode and it caused the police to come looking for him.