The user enroll search feature is kind of quirky in eClass Moodle; Therefore, the surest way to confirm that a user is the correct person you are trying to enroll is by knowing their CCID.  The searches return on either the full name, CCID, or email address. Note that email addresses associated with eClass accounts are of the form ccid@ualberta.ca. Searching for an email address alias formatted as firstname.lastname@ualberta.ca will not return the user your are searching for. This is different from BB Vista.

This is further complicated by the search strictness and the addition of preferred names to moodle. For example, if a user has specified a preferred name, the moodle full name would display as PreferredName (Legal FirstName) Last Name. Eg. User with legal name David Laurie goes by Dave so he enters his preferred name in Beartracks as Dave. Moodle then pulls this out and displays the user full name as 'Dave (David) Laurie'. Now searching for Dave Laurie or David Laurie will not return the user as the string is broken up by the legal name and brackets ie.'(David)'. So in some cases, you need to shorten your search to only a first or last name and pick the correct one from all the returned users.  

Searching like this sometimes requires verification to confirm that a CCID or email address belong to the person you are trying to enroll. You can use U of A's 'Find a person' from the top of the U of A home page for this. When you search for people on that service, clicking on a particular user will show their preferred email address in the main panel, often the firstname.lastname@ualberta.ca alias. The user view will also show the user's CCID in the string of the address bar. So if you searched for Dave Laurie, the end of the url in the address bar is '?type=simple&uid=true&c=dlaurie' so you could verify that the CCID dlaurie goes with the email alias dave.laurie @ualberta.ca which appears in the main panel.