By default, Microsoft Edge displays the active tab's title on its "title bar":

And StarDock Groupy mirrors this for its own tab title:

But when you right click Edge's title bar, it also offers the option: "Name window":

This means you can assign a custom fixed name to the window.

This will not change, no matter what tab is active.

However, utilizing this "Name window" option causes the relevant StarDock Groupy tab to shrink and display absolutely no title at all:

I would like StarDock Groupy to respect the name I give the window.

....

P.S.,

You may ask: "Why not just rename StarDock Groupy's tab manually?"

Because StarDock Groupy forgets custom tab naming, after the program is exited.
Whereas Edge's "Name window" option carries over, even after restarts (when Edge is set to restore previous sessions).