The Task Bar button usually matches the window title (the title displayed in the window title bar). This can be changed with a script. For example, to blank the title on this page, copy the following script, paste it to the address bar and press Enter.

javascript:void(document.title="");

I'm not sure of the most convenient way to automate that. One option would be to use the Greasemonkey add-on and create a userscript that applies it to every page.

https://addons.mozilla.org/en-US/firefox/addon/nightly-tester-tools/

Nightly Tester Tools has an option to create custom Titlebar text using the "Custom Titlebar" window in Tools > Nightly Tester Tools > Customize Titlebar. You can use the "Variables" listed or just type any old thing you want to display on the Titlebar or even an combination of Variables and your own wording.

thanks for your help.

@jscher2000, your method did remove the title, but it also removed it from the tabs. a bit too 'destructive' for my needs.

@the-edmeister, exactly what i was looking for. i am surprised this isnt already an configurable option within firefox (in about:config or similar).