NameMapping File and Git Source Control

That's exactly it.  LinoTadros is really right and one person should do the mapping, but with our team we were willing to take the risk of each person doing their own mapping.  We choose a mutually good day to give all the mappings to one person and they merge and resolve conflicts  with the TC tool.  That copy is passed back to the team and we run our tests with it and adjustments are made if necessary.  The new copy that works for everyone is then checked in.  Any of us are capable of doing it, so we avoid problems with vacations and such.