Group name and Tag name on top of tag page

You can display the group name with

[tag_groups_info group_id=1 info=label]

see https://documentation.chattymango.com/documentation/tag-groups/tag-groups-info-tag-clouds-and-groups-info/tag-groups-info-shortcode-parameters/

The tags are part of standard WordPress, so you could ask your theme author where in the template to make a modification.

and group name + tag name ?

This one should work in the tag archive template of your theme:

<?php

$tag_name = single_tag_title( "", false );
echo do_shortcode('[tag_groups_info group_id=1 info=label]') . ' ' . $tag_name;
?>