The enclosed patch will enable Elgg to search over usernames (users.username) in addition to names (users.name). Additionally, it uses the icon-based results display consistent with the profile plugin (since that's where I copied it from, after all).
Note that I turned off the catch clause at the top that uses the MATCH...AGAINST syntax if we're on MySQL. MATCH...AGAINST doesn't do sub-word substring searches, so it really shouldn't be used on matching names. For example, you can't search for "just" and come up with "justin" as a result. Hence the move to the LIKE syntax instead. I've left the old code in this patch, but maybe it ought to be taken out entirely; that's your call.