Several years ago eBay deliberately stopped allowing sellers to change store URL and it's caused a lot of frustration among sellers.
The only method now available to sellers to change the Store URL is to close the store and then open a new store with the new name and URL. Your listings will continue to run without the store.
Check your subscription early termination fee (link) before deciding when to close the store.
After closing a store, eBay will hold that name and URL for 30 days in case you want to reopen the store. Since you have already changed your store name to your "permanent" name, you would have to wait over 30 days to use it on a new store and get the new URL. Keep in mind that someone else could grab the name after 30 days so you'll want to schedule alerts in your calendar.
There are two ways to handle the 30 day waiting period:
1) Close your store, wait over 30 days with no store, and open a new store with the permanent name to get a matching URL.
2) Change your store name to something temporary. Use that temporary name for over 30 days while waiting for your "permanent" store name to become available again. Then close the store with the temporary name and open a new store with the permanent name.
After opening the new store, your listings will be imported, but you will need to manually start over by re-creating your store categories, banner, about section, etc.
