1. Choose Bookmarks > Organize bookmarks.
2. In the Library window, select the bookmark or folder you want to rename.
3. In the Name box, edit the name of the item. The change takes effect as soon as you click anywhere else.
4. Close the Library window

Another way to do this is with the Bookmarks sidebar:

1. Choose View > Sidebar > Bookmarks.
2. Right-click the bookmark or folder you want to rename, and click Properties.
3. In the Name box, edit the name of the item.
4. Click Save.

For whatever reason, in Mac OS X Snow Leopard, the first solution does not work - in that the pane that results does not include the "Properties" option.

However I found the second solution to be effective.

Hopefully, someone at Mozilla will investigate what's going on and remedy the situation.

Many thanks to JMSwisher

I'm using FireFox 3.6.16 (latest version) and I cannot use your first solution. There is no 'Name' place to type anything in. I tried right clicking for 'properties' or 'rename'.

Second option works if you can find out how to open the sidebar! It's not in the Bookmarks menu (or the Bookmarks 'View' menu). It's in the main 'View' menu (I was confused as to which 'View' menu you were referring to =)

Thanks for both options!

You should be able to make the change in the Library if you select the parent folder (e.g. Bookmarks Menu) via the left pane. Then you can highlight that folder in the right pane and make the change in the Details pane at the bottom right. That is how it works in the Library (Bookmarks Manager). There is not Properties in the right-click context menu in the Library. The right-click context menu (Properties) can only be used in the sidebar on Mac (and probably on the Bookmarks Toolbar).