Hi,

I'm looking for the OEM positive terminal black box of the battery, see photo attached.
Where can I find it?
What is it's official name?
It has a part number?

 

I believe that would be considered a dealer item. You might need to purchase the entire cable. What you can do is place the protective cover where it goes and use a plastic tie or two to hold it in place. All that cover does is to prevent any metal from coming in contact with that post of the battery
It is made so it can be lifted off the post to check for corrosion or attach jumper cables if necessary It is a safety feature and nothing more. Doesn't even prevent corrosion.

Newer vehicles require a resetting procedure when replacing the battery so the computer knows it has been changed and controls the charging system accordingly.