Sort and paginate custom post taxonomies alphabetically

As I stated in comments, you can either use usort() to sort the returned array of terms, or you can just use wp_get_post_terms() which is already sorted by default by name in ascending order

$terms = wp_get_post_terms( get_the_ID(), 'brand' );
var_dump( $terms );

EDIT

Here is an example with usort() and get_the_terms()

$terms = get_the_terms( get_the_ID(), 'brand' );
usort( $terms, function ( $a, $b )
{

    return strcasecmp( $a->name, $b->name );

});