genius55 is correct that the horse doesn't have an authenticated name and also about the association with hobby horses. So the most usual name for the horse is Dobbin (alternative version of Hobbyn or Hobbin)
PS I think that is why old nags are sometimes called Dobbin, because Robin Hood was poor and therefore wouldn't have had a flash ride to rival the Sheriff's horses
indeed a wonderful answer, but again i beg to differ coz in the robin hood theme by bryan adams, the singer distinctly (to me) sings 'Dobbin, it's not worth trying for')