How can I convert from a SID to an account name in C#

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.

The SecurityReference object's Translate method does work on non-local SIDs but only for domain accounts. For accounts local to another machine or in a non-domain setup you would need to PInvoke the function LookupAccountSid specifying the specific machine name on which the look up needs to be performed.

System.DirectoryServices.AccountManagement.UserPrincipal class (msdn link) has a static function FindByIdentity to convert an SID to a User object. It should be able to work both against the local machine or an LDAP/Active Directory server. I have only used it against active directory.

Here is an example that I have used in IIS:

// Set the search context to a specific domain in active directory
var searchContext = new PrincipalContext(ContextType.Domain, "YOURDOMAIN", "OU=SomeOU,DC=YourCompany,DC=com");
// get the currently logged in user from IIS
MembershipUser aspUser = Membership.GetUser();
// get the SID of the user (stored in the SecurityIdentifier class)
var sid = aspUser.ProviderUserKey as System.Security.Principal.SecurityIdentifier;
// get the ActiveDirectory user object using the SID (sid.Value returns the SID in string form)
var adUser = UserPrincipal.FindByIdentity(searchContext, IdentityType.Sid, sid.Value);
// do stuff to user, look up group membership, etc.