For the site I am working on, we are in the process of improving our URLs for one type of resource - specifically, moving away from numerical IDs toward unique, descriptive
Your first option is probably the best.
Searching for users by ID:
/users/id/48573
Searching for users by short name:
/users/name/thisisausername
If they leave out that path parameter, you could always default to your new short username format.
Another option that I have seen quite a bit is to use query parameters like the following:
/users?id=48573
/users?name=thisisausername
I think the first looks a bit cleaner and more readable.