This seems to have happened recently on a friends system. It's a generic machine, probably two years newer than mine.
She went to google, selected a site, clicked on 'Bookmark' and then tried to create a new folder, but was unale to create a new folder. I also tried it with the same result. It will bookmark as the URL name appears, but I cannot either delete, or type over that name. This is in Firefox.
In IE 11, she does not have that problem - using FF version 44.0.2
By clicking on the hollow star on the bookmark toolbar or,
By right clicking on the page you want to bookmark and then clicking on the hollow star?
You should be able to right click on any bookmark and near the bottom of the context menu you will see Delete; To change or rename a bookmark click on Properties below Delete, when the properties dialog box opens for that bookmark, left click anywhere in the Name field of the bookmark to set the blinking cursor. From there that field acts as a text editor.
She could also go to >History in the Menu bar >Click on Show History >A new window called Library opens showing all history and editing can be done there.
She should also be able to right click on any existing Folder or anywhere within the bookmarks toolbar and see the New Folder selection
The method she and I have used for quite some time and it has worked fine. I went back and tried again on my machine and there's no problem. I'm considering uninstalling her version of FF and try a reinstall.
Open a web page
Click on Bookmarks
Next window click on "Bookmark this Page"
In "Page Bookmarked" , click on down arrow in Folder. Select "Choose", click on "new folder" button.
In highlighted area enter name you want, then click the "Done" button'