What is this part called and where do you get a new one?

It looks rusted/corroded

 

Battery Terminal. You can get a new one but if you take it off and clean it up with some baking soda or even a Coca Cola and a wire brush be like new again!

 

Do you soak it in coke

 

Add 1/2 cup of baking soda with water in a jar mix well, soak the battery terminal in it, it will fize which is the battery acid being neutralized, when the fizzing slows down remove and use the wire brush to start cleaning it, mix the solution again and soak again, then wire brush again, keep repeating until no more fizzing and it looks good to you.

Use the remaining solution mix well to pour over your battery top to neutralize any acid on it, rinse everything with fresh water, avoid getting any splashes on your clothes, the acid will eat holes in most fabrics, the acid will not hurt your skin with brief exposure, just rinse it off.

 

You could do that or just pour it over. I've used both Coke and Baking soda. Both work!

 

Simple Green works well for cleaning battery terminals also.

 

When it's clean, you can coat it with Fluid Film to keep it that way.

 

Or LPS 3, ACF-50 too

 

I’ll be the odd guy out and say it looks more like dirt and dust stuck to some corrosion inhibitor that was sprayed on at one point . I bought a new Nissan and sprayed the terminals with a marine anti corrosion terminal spray that dried a waxy yellow color .
After awhile they looked kind of like the OP’s terminals . The first time I took it in for service the “tech” wrote that the terminals were corroded and needed cleaning .
Just my 2 cents .

 

I agree this doesn’t need to be replaced. You could just take one of those harbor freight metal toothbrushes and clean the contact points or a small piece of fine sand paper and it will clean up like new. The contact points are what counts if you aren’t looking for pretty

 

Your battery connections ate good to go and look good, too. I just recently upgraded mine so it looks less like a spider's web and it has worked great thus far. You don't need to do this unless you like spending money, though.