All Tennis Players How Many Grand Slams Has Reginald Doherty Won? Reginald “Reggie” or “R. F.” Frank Doherty (14 October 1872 – 29 December 1910) was a British tennis player.Reginald Doherty has won 4 Grand Slams. FacebookTwitterEmail How Many Grand Slams Has Madison Keys Won? How Many Grand Slams Has Jannik Sinner Won? How Many Majors Has John Isner Won?