See here for a good answer:
The best way to resolve display username by SID?
The gist of it is this bit:
string sid="S-1-5-21-789336058-507921405-854245398-9938";
string account = new System.Security.Principal.SecurityIdentifier(sid).Translate(typeof(System.Security.Principal.NTAccount)).ToString();
This approach works for me for non-local SID’s over the active directory.