Restrict partially matching usernames

There’s a validate_username filter hook that is used by validate_user() which is in turn used by register_new_user().

So you can disallow usernames containing admin or other prohibited terms:

add_filter( 'validate_username', 'wpse257667_check_username', 10, 2 );
function wpse257667_check_username( $valid, $username ) {
    // This array can grow as large as needed.   
    $disallowed = array( 'admin', 'other_disallowed_string' );
    foreach( $disallowed as $string ) {
        // If any disallowed string is in the username,
        // mark $valid as false.
        if ( $valid && false !== strpos( $username, $string ) ) {
            $valid = false;
        }
    }
    return $valid;
}

You can add this code to your theme’s functions.php file or (preferably) make it a plugin.

References

• validate_username filter hook
• validate_user()
• register_new_user()
• Writing a plugin