A couple of strategies for managing NameMapping came up at the recent connect conference.
1) Have one person designated as the "Master of all NameMapping". Anything that needs to be mapped, they map. They do the mapping ahead of time before automation against the components is started. Then all automation developers download the latest mapping file before working on that piece of the application under test.
2) Have one person in charge of "merging" NameMapping. No NameMapping is actually checked in to your SCM from the individuals. Instead, they do their mapping and then send their NameMapping.tcNM files to another party. That person then has a special project in TestComplete whose sole purpose is to use the built in TestComplete "Merge" feature to merge those individual namemapping files into the central one, resolve all conflicts, and then check in to SCM. Then, once the merging is complete (sounds like a bad sci-fi trope...), the individuals download the latest NameMapping. I believe Marsha_R uses this method.
As for the other files within Regions, Files, Objects, XML, the way we handle that here is that we a) don't put stores files in different directories. We just store them in the default project folder structure and use a naming convention to describe what the files are. And b), no two people are working on the same file at the same time. This is a bit harder to control "automatically", but generally it's a matter of making sure that if I am working with XMLFile1, no one else is at the same time. That way there is no conflict and we don't have to worry about it. This might not work for you, depending upon how you structure things.
