The etymology of "Yazidī"
I need you all to listen very well:
The term Yazidī / Ezidī does not derive from the name of Yazīd ibn Mu'āwiyya. Because it CANNOT. Yazīd- > Yazid- DOES NOT happen because it CANNOT happen. We don't have shifts from long i to short i or vice versa in Kurdish or other well known Iranic tongues.
First of all, the NK term "ezidī" is from "yazidī" because NK reduces initial y- very often and in the case of ya- even shifts them to e-:
yatīm > etīm (orphan)
yān > ān (or)
yārīkar > ārīkār / ālīkār (helper) (Yes, the "āl-" in ālīkār is cognatic to "yār" (friend) in other Iranic tongues and ālīkār is derived from a compound from "yārī" (friendship, help) + kār (work, deed but here: doer, worker)).
etc.
Secondly, the God of the Yazidī is called "Ezdā" in their own NK speech which obviously is also from "Yazdān" which is a well known word for god in Western Iranic languages. The word directly and completely derives from Zoroastrian culture because Prophet Zoroaster refused to acknowledge any other god than Āhurā Māzdā and called the other gods unholy and undivine. This is why the original words for "god" in Iranic like "baga" are not used in Awistan and why Zoroastrian-influenced Iranic "dew" (in Kurdish, "dīv" in iranian new persian) means demon instead of god although it derives from Proto-Iranic daywas and is cognatic to Latin deus or Hellenic theos both meaning god. Meanwhile Eastern Iranic tongues that were not under influence of the Zoroastrian religion still have the word "dew" with the meaning "god".
But as there were still holy and divine beings in Zoroastrianism, especially as they were also brought back after Zoroaster in a less divine spot, they were called "yazata-" which means "to be worshipped" or "worshipped one" and is cognatic to the Kurdish word "jazhn" meaning "festival", "celebration" which derives from yasna (same yasna as those of the Zoroastrian literature).
Yazata- > Yazad > Yazadān >Yazidān > Yazdān
Yazata- > Yazad > Yazid > Yazd
Yasna- > Yashn > Jashn > Jazhn
The more colloquial meaning of jazhn together with its proper SCNK and Persid sound shift of initial y > j makes sense, as opposed to a holy word with its more so retained meaning "yazd-" and the sound shift not applying to it makes also sense I argue because the speakers would be less inclined to go with such a strong differene in pronounciation and would keep to the old pronounciation (yazd instead of jazd).
Now, the Yazidī are obviously called after their god Ezda ( < Yazdān). Probably when Yazdān was Yazidān yet and possibly even when one of the forms of Yazidān was "Yazid". So, "Yazidī" simply means "Of god" in NK Yazidī terming. Or "adherent of god". Or "People of God". This is a pretty normal naming.
But it is important that people know and understand where their name came from and how it changed from its original form.