I have several NTSC-U/C and NTSC-J versions of the same game. When I try to add the game it will only allow me to add the North America release title.
For example Riglord Saga for the Saturn. I can add it as Blazing Heroes, but I want it displayed as Riglord Saga on my game list with Japanese art.
Also Seiken Densetsu 2 for Super Famicom will only let me add it as Secret of Mana SNES.

Is adding alternate region titles even possible?

You can select the region you wish to have during quick add. As far as JP box art and names, that information has to be loaded into the site.

Feel free to to use the thread below for requests such as those you have listed already.

https://www.completionator.com/Forum/PostList/3280?page=1

I've updated Blazing Heroes and Secret of Mana was already done. When adding the game to your collection select the region you want. When you see the games in your collection, their region specific name should show (again this is the information has been added).