Yes you can do that; just copy
/usr/share/games/minetest/games/minetest_game to your own folder (like .minetest/games/manglefox).
Then, in that folder, locate the game.conf file and change the name to whatever you want.
You can also change the menu/header.png and menu/icon.png files. Those are used in the UI to visually identify your game (at least, add something in those images to see the difference).
To change an existing world:
- first, make a backup of your world folder !
- next, in the world folder, there is a file named
world.mt. In that file, locate the following line and replace "minetest_game" with your game folder name:
Your phone or window isn't wide enough to display the code box. If it's a phone, try rotating it to landscape mode.