His father Alois was illegitimate and used his mother's surname Schicklgruber for the first 39 years of his life before changing his surname to that of his (then dead) stepfather Johann Georg Hiedler.
The surname Hiedler and its variants Huetler and Huettler also existed in the family of Alois' maternal grandparents.
It is thought that the spelling of Hiedler was probably changed to "Hitler" by a clerk during registration of the name change.
I believe Hitler had an English born nephew who regularly toured the USA before the war giving lectures about his uncle. He changed his name at the outbreak of the war and even served in the US Navy towards the end of WWII. Three of this man's four sons still live in the USA, but none have reclaimed the Hitler surname.
Another branch of the Hitler family, again in the USA, have sued for access to the proceeds of Hitler's estate, particularly the rights to Hitler's book, Mein Kampf.
Certainly Hitler would be an unfortunate surname to have in Germany or Austria today - unfortunate anywhere perhaps - but worse would be Schicklgruber. No wonder Alois preferred Hiedler.....