Doesn't answer why it changed mid-career though?
This is an educated guess:
-Native speakers please correct me if I'm wrong on any of this-
Mr Khan himself has said that he prefers Younus, and he has always spelled it as such,
As far as I can tell (I could be wrong here), there is no equivalent written letter to a short i (as in "bitter") in hindi/urdu, even though it is spoken in-between consonants. (there's a short i but it's pronounced more like a short ee, to my ear). That short i as in bitter is not so much thought of as a vowel.
Consider also that I, Y and EE are the same letter in the Arabic script. And in fact most short vowels are dispensed of.
I suspect Younus' objection is that when he sees Younis he thinks it means Youness/Younees, as in Loch Ness, or Younis like how a Spanish person would say it. But we in English would pronounce Younus and Younis exactly the same.
My guess is that Younis was initially translated in broadcast by a native English speaker who knows that Younis and Younus are pronounced the same in English (at least NZ English). And then Younus objected based on what he considers the pronunciation of Younis spelt like that to be.