Typically when you're searching for a user (student or otherwise) in Moodle, you're looking for them in order to manually enroll them in your course. If you're unable to find them, that almost always means that they have never logged in to Moodle. When anyone's account for Moodle is created, it's doesn't actually, fully come into existence until the user logs in to the account for the first time. If you're having trouble finding a student in Moodle, please reach out to them and encourage them to log in to their Moodle account. As soon as they do, you'll immediately be able to find them in the user search.