We have a similar issue in English. British, American, Australian, New Zealand, South
African, etc.
The three varieties of Kurdish are not mutually intelligible (says the oracle
https://en.wikipedia.org/wiki/Kurdish_languages#Subdivisions here) and they ought to have
terms for all three that they can use.
It is wrong to say that any one of the Kurdish languages is “more Kurdish” than the
others.
Perhaps they will respond to something like this.
Michael