From MozillaZine Knowledge Base

Using an extension

It is possible to change the wording using an extension such as Firesomething or Titlebar tweaks (both by momokatte).

Manual procedure

1. Go to your Firefox application folder. Then, go to a folder that's called "chrome". Copy that folder somewhere else for a backup.
2. Within the "chrome" folder, there is a JAR file called "en-US.jar". Extract it (We assume you use US English Firefox). You need to have some software that can extract JARs and repackage them. Examples are WinRAR, 7-Zip, Winzip, etc. Alternatively, under Windows XP, you can rename it to "en-US.zip", use the built-in unzipper, make your changes, and change it back to "en-US.jar" when you're done.
3. In the file that you extracted, there is a "locale" folder.
   • Firefox 1.0: Navigate to locale\en-US\global.
   • Later Firefox versions: Navigate to locale\branding.
4. Open "brand.dtd" file.

There, you should see something like this:

<!ENTITY  brandShortName        "Firefox">
<!ENTITY  brandFullName         "Mozilla Firefox">            
<!ENTITY  vendorShortName       "Mozilla">

<!ENTITY  releaseURL            "http://www.mozilla.org/products/firefox/releases/1.0.html">

You may edit that to something like this:

<!ENTITY  brandShortName        "Browser++">
<!ENTITY  brandFullName         "My Firefox">
<!ENTITY  vendorShortName       "Mozilla">

<!ENTITY  releaseURL            "http://www.mozilla.org/products/firefox/releases/1.0.html">

Then, repackage everything back exactly how it was and open up Firefox. If Firefox has issues, just restore the backup copy and try again.