I've found four doctors who appear to have been Queen Victoria's doctors over various periods of time.
Sir William Henry Broadbent, Bt., KCVO, MD, Physician Extraordinary to Queen Victoria (1896–1901)[1]
Sir Henry Thompson, 1st Baronet, FRCS (1820–1904), Physician to Queen Victoria
Sir Thomas Grainger Stewart, FRSE, FRCPE (1837-1900), Physician-in-Ordinary to the Queen in Scotland from 1882
George Steward Beatson ( - 1874) Honorary Physician to the Queen
If you click on the link below you should be able to click on each name for further information on that name.
https://en.wikipedia.org/wiki/Physician_to_the_Queen