You need to be careful overriding the entire array as WordPress may add new items from time to time…override each specific value instead like this:
add_action( 'init', function() {
global $wp_taxonomies;
$wp_taxonomies['post_tag']->labels->name="Groups";
$wp_taxonomies['post_tag']->labels->menu_name="Groups";
$wp_taxonomies['post_tag']->labels->singular_name="Group";
$wp_taxonomies['post_tag']->labels->search_items="Search Groups";
$wp_taxonomies['post_tag']->label="Groups";
}, 1 );
I showed a few examples just do it for all the values you wish to change.