If you set the tab label to %P it will show the full path (documented here).
Note that there is a limit to how wide the tabs and their labels will be, and the path will be truncated with "..." in the middle (and sometimes at the end as well, if the last component is very long), to prevent the tabs becoming ridiculously wide.
Drop this simple script add-in into Preferences / Toolbars / Scripts to make all new tabs use %P for their names by default:
Simple Tab Labels.js.txt (1.0 KB)
(The script's configuration window can be used to change the %P to something else if you want.)
For more complex tab naming, the Tab-Labelizer script may be of interest.