Here is one of the quotes I have found in online research.
"KYLE: Variant form of Hebrew Kelila, meaning "crown" or "laurel." Used as a Yiddish name."
I have seen that sometimes Kyle is spelled Kiel, Keli, Keil or even Kil or Coil. My Mother used Kyle as her maiden name.
I base the knowledge of my Maternal Grandfathers ancestry on both what my Mother told me, and what is in her medical records, from what she told her doctors. First of all she told me that even though her Fathers family came to America via Ireland, that they were from "White Russia", and they had to "flee from the Czar, to save their lives". At the time she did not mention them being Jewish in ancestry, and I did not know that White Russia was also known as Belarus, which is right in the Pale of Settlement in Russia.
But when I found out after she was gone that she had told her doctors that she was Jewish, and they tried to see if that information might help to understand the auto-immune condition that was killing her, did I really get confirmation, from her at least, that her Fathers people were Jewish in ancestry. In America they were no religion, apparently they were political, rather than religious.
So, I do not know for sure, but I am trying to piece it together. I may need to trace records in Ireland, form when they entered there, to see what is said about the family origin in Russia.