Just anecdotal, I knew the name "Deepwater Horizon", but was very aware that BP was the responsible party. There was a lot of discussion of not buying gas from BP stations for a while afterwards and it became a common subject again when they started rebranding and painting their stations green.

Dunno what happened behind the scenes with the naming, but I'd say most people in my area associated it strongly with BP and am pretty confident that BP was implicated on the NPR radio station I listened to.