You can use tab_selected(int tab) signal from each tab and trigger a one shot timer whenever a click event is received. If a click occurred while the timer is active (double click), make a pop-up that contains a LineEdit, confirmation button and a cancel button. when the user confirms, use set_tab_title() to edit the title.
Make sure you pass up the tab number from tab_selected(int tab) so that you know which tab to change its title.
This approach looks a bit different (and kind of old-school), but it’s simpler to code.