No. In GeoDirectory v2 a listing’s URL slug is set when the listing is first published, and it stays the same when the title is edited later. That applies whether the owner edits the listing from the frontend or an admin edits it in the backend, and it’s the same way WordPress treats posts and pages.

GeoDirectory v1 rebuilt the slug from the title on every frontend edit. Current versions don’t.

Changing a listing URL on purpose

Admins can still change a slug. Edit the listing in the backend (Places > All Places) and change the URL slug in the editor, the same way you would for a post. Listing owners can’t change the slug from the frontend form.

Listing URLs can also include the category and the location, depending on your permalink settings. Moving a listing to another category or changing its address can therefore change its URL too.

Keeping old links working

Leave Enable 404 rescue ticked at GeoDirectory > Settings > General > Developer. It’s on by default. When someone visits a GeoDirectory URL that no longer exists, GeoDirectory tries to find the listing or category and redirect to its current URL, which also tells search engines about the change.