You cannot do that unfortunately. There may be add-ons that help with that, but it's not part of Firefox.

Hi jpickett, what appears on the tab is the contents of the <title> tag in the page (well, as much as will fit of it). If you see the site address instead of normal text, the page may not have set a title.

As Tyler mentions, Firefox doesn't have a feature to modify page titles. Depending on the frequency and complexity of your needs, you might use a number of workarounds, including a bookmarklet -- a script you save in your bookmarks that only modifies a page when you run it; a user script -- a brief program you apply to pages using an extension like Tampermonkey, Violentmonkey, or Greasemonkey; or a dedicated extension.

Here's a discussion from another thread that may give you some ideas: How do I edit what appears in the browser's title bar? (I don't people to see my gmail address when on the gmail tab).

Thanks for the feedback. Mozilla, are you monitoring this? Perhaps a modification in the foreseeable future? Hope so.