According to John Toland's "Adolf Hitler: The Definitive Biography" Hitler's father was born out of wedlock and originally named Alois Schicklgruber (his mother's last name) and wanted to change his last name to that of his stepfather Johann Georg Hiedler (who may or may not be his biological father. For unknown reasons it was spelled Hitler instead. So as a result there weren't many Hitlers around. Most of his siblings died young except for sister Angela and Paula (who lived as Paula Wolff) and half brother Alois Hitler Jr. (his son Heinz Hitler died in the war at 21, his other son William Patrick was born to a English wife and had British citizenship. He changed his last name to "Stuart-Houston" and fought against the Nazis in the American navy.

Not very common. As Ian Kershaw explains in his biography "Hitler 1889–1936: Hubris" Hitler's father, Alois, was born a 'Schicklgruber', and only changed his last name to "Hitler" later in life, and the age of 39. The weird thing, which apparently isn't totally clear still, is why!

We know that Alois (or Aloys) was an illegitimate child, and the intent to change his name was possibly to honor the man who raised. But his stepfather's name was Johann Georg Hiedler. Johann married Maria Schicklgruber when Alois was five, and Maria died when Alois was about 10. Johann would die a decade later, and regardless Alois was raised mostly by Johann's brother - also a Johann, Johann Nepomuk, who effectively raised him in his teens, but seems to have never formally adopted him (Also notable that Johann went by Hüttler, not Hiedler, at times). It is possible that Johann Nepomuk requested Alois to change his name, being along in years and with no male heir of his own. It is also possible that, as documents were changed to this effect, he was declaring that Johann Georg was his legitimate father, and not just his stepfather, which Alois and other witnesses stated Georg had attested to prior to his death 19 years earlier. The true reason can only be guessed (Whether Georg, Nepomuk, or someone else was the father is still something people debate apparently).

What we do know is that, for whatever reason, the legal documents, instead of reading Hiedler or Hüttler, note the alternative spelling of Hitler. Again, we don't know why he chose that spelling, and can only surmise. Kershaw notes the possibility that Alois Hitler viewed his chosen spelling as "less rustic" than the two used by his father (?) and uncle (?), but also that Hitler might simply have told the notary the name he wanted, and gone with the spelling that the notary chose without complaint. We simply don't know.

Anyways, what this long digression is to say is that Hiedler, Hüttler, as well as Hütler and Hietler. They roughly mean "smallholder", and were interchangable to the point that some individuals switched between them, as with Johann Nepomuk. Hitler is also a form of that name, but as far as I can find, a less common variation. We don't know the reason for it, but that particular spelling, in Adolf's family tree at least, only begins with his father. As such, the (as named) Hitler family tree is a very small one that only dates to the late 19th century.

As noted, this is all from Kershaw.