No, it would be the name of whomever paid you like Continental for example. Don't forget to go to the Royalty section, so you can deduct things like production taxes and property taxes if you own the land. It's also where the 15% depletion allowance is calculated (automatic).
Your 1099-MISC will be reported as a gross amount, but you likely received less so look over your statements and deduct the difference as expenses. And lastly, OK allows for an additional 7% depletion allowance (22% in total), so visit that adjustment to income section in the OK state return to take advantage of the allowance.