[BBcue-Z]

The best I could tell from your last picture, this looks like a Rib roast- see chart below, first cut below the neck. It may have been cut a little low, because I see the end of the rib cage and the start of the tenderloin (the small circle in the last pix). The large circle is the loin.

I prefer to cut the rib section into rib chops and direct grill them to medium rare. Cooking it whole may not be a bad idea, just matter of preference.