If you reset the User Data Folder in the game to default it should pick up the databases saved by the editor. You could also change the User Data Folder in the editor to be the same as in the game, that way any new databases will be saved to the correct folder, all though it won't find the databases you have already saved unless you manually move them to the new location.
You can only specify a name because the databases needs to be in a specific folder for the game to be able to find them, so the editor will make sure to put the database in the correct place, as long as you haven't changed the User Data Folder in either the game or the editor.