How can I get DOMAIN\USER from an AD DirectoryEntry?

This assumes that results is a SearchResultCollection obtained from a DirectorySearcher, but you should be able to get the objectsid from a DirectoryEntry directly.

SearchResult result = results[0];
var propertyValues = result.Properties["objectsid"];
var objectsid = (byte[])propertyValues[0];

var sid = new SecurityIdentifier(objectsid, 0);

var account = sid.Translate(typeof(NTAccount));
account.ToString(); // This give the DOMAIN\User format for the account