FF tweakers might be interested in this.
I only found partial answers when googling.
This is about when the Firefox search box is empty, the name of the current search engine is displayed next to the icon. Pointless, unless you have so many search engines you can't recognize the icons!
Remove the text, so only the icon is left:
1. Backup the default .xml files that are in this folder: C:\Program Files\Mozilla Firefox\searchplugins
2. Edit the ShortName in the first .xml file as (for example): "<ShortName>Google</ShortName>" to "<ShortName> </ShortName>" (1 blank space) and save.
3. Edit the next search engine's .xml file with 2 blank spaces for the "ShortName" instead of 1. Then the one after that has to have 3 spaces, etc.
4. Delete the file: C:\Users\-username-\AppData\Roaming\Mozilla\Firefox\Profiles\-------.default\search.json
5. Run Firefox. The "search.json" file is recreated with the changes.
If there are some search engines missing, or the changes have not fully taken effect:
Search dropdown > Manage search engines > Restore defaults button > OK.
Do the changes over as above. Don't forget to delete the search.json file. Restart Firefox.