I absolutely love the top bit of the rib eye (just above that little round lump of fat. I find the main bit of the steak a bit underwhelming but man I'm crazy over the top part. Does anyone know if that part of the steak has a proper name so I could get just that part?

Don't know the name of it. If it was trimmed it would just be classed as an offcut wouldn't it?
Not sure a butcher would be happy to trim a whole rib joint to get that piece of meat off it.

You could ask this guy
http://www.donaldrussell.com/blog/ar...a-ribeye-steak

No I can't imagine a butcher would. I'm shocked it would be classed as an off cut its the best steak I have ever tasted! lol

Oh I love Ribeye, I was going to get some for the weekend

It would only be classed as an offcut because it's not a recognised cut. Offcut doesn't necessarily mean the meat is crap.