Which famous race was nearly named The Bunbury ?

I believe it is the Derby Stakes at Epsom.

Correct,except it's not called the Derby stakes but simply 'the Derby'. Two friends, Mr Bunbury and the Earl of Derby, drew lots to decide whose name would be given to the new race. Derby won or we'd have the Bunbury and the Kentucky Bunbury, no doubt.Pity: Americans might have been able to pronounce 'Bunbury' . (Derby, whether it be the town in the English midlands, the horserace or the Earldom is pronounced 'dar-bee', not 'durr-bee')However,Mr Bunbury drew first blood: his own colt won the first running of the Derby, in 1780. The equivalent race for fillies had been run the year before. It was named the Oaks, after a house that Mr Bunbury owned.

The Derby was run again today, June 2nd. Our most famous and popular jockey, the Italian born Frankie Dettori, on Authorized, won the race for the first time at his fifteenth attempt.He's won just about every other big race but hitherto the Derby had eluded him. He is the only British jockey living who has had a statue erected in his honour. It celebrates his winning all seven races on one day at Ascot.