string directoryPath = "WinNT://somedomain/someuser";
string fullName;

DirectoryEntry directoryEntry = new DirectoryEntry(directoryPath);
if (directoryEntry.Properties["FullName"].Value != null)
{
   fullName = directoryEntry.Properties["FullName"].Value.ToString();
}

One issue with this code is that when "somedomain" actually corresponds to the local machine name (because your are trying to retrieve the "FullName" of a local account), it can take an extremely long time to run. This is probably because the underlying framework is off trying to find a domain controller before falling back to the local security store.

To work around this, consider code that would look like the following when formulating the directory path:

string[] identities = windowsIdentity.Name.Split('\\');
string directoryPath;
if(Environment.UserDomainName.Equals(Environment.MachineName,StringComparison.OrdinalIgnoreCase))
{
   // special case needed for "off domain" case.
   directoryPath = "WinNT://localhost/" + identities[1];
}
else
{
   directoryPath = "WinNT://" + identities[0] + "/" + identities[1];
}