Since there is no signs, we shall add the names how the local people say it in the spoken language. The people of the Town speaks mainly Arabic. And the 'name' tags inside this town shall be according to that, Which follows the on-ground rule. If there is a shop for example that has the banner in Kurdish only, or mainly, it shall be put in 'name' no problem, but if there were no signs, we use the local spoken language.   
   
The town of Kifri is mixed between Arabic, Turkemen and Kurds, previously Jewish too, that doesn't mean that each ethnic group in this town speak it's own language, as you know many parts of Iraq the Kurds speak only Arabic, but here in Kifri, it's mainly or mostly Arabic.     
   
The town is part of Diyala Governorate by law, it is not part of the Kurdish region, therefore it shall be mapped according to the legislation of administration of Diyala Governorate.    
The Mayor of the town is Sahir Ali Jasim, which he is an Arab, and appointed by Diyala governor.  

If you are a Kurd and you go to the town of Kifri, they will speak with you in Kurdish, if you were Arab, They will speak with you in Arabic. It is that simple.     
     
About the links you sent, I shall inform you dear that Facebook, YouTube and Google Maps shall never be used as a source for mapping in OSM, it can be used in a comment to validate a point in discussion I guess yes, but never in mapping or tracing etc..    
Google Maps, shows you the names of object in your language, the one you are using in your device thus it will show you in Kurdish.   
Since you mentioned Google Maps, I will give you examples from it. The main name of the Town in Google maps in Arabic, you can use VPN and change to any foreign language and you will see that Google say the Arabic name under it, which indicate the local language. See: https://maps.app.goo.gl/ajSA82kGWpx46Jhj8    
See this screenshot https://i.ibb.co/mCfPYtH/image.png , if you selected any language, it will say the name of the town in that language and under that it will show the local name in Arabic. But if you have the language in Arabic, it will not show you any other languages.     
    
Another thing worth mentioning, the people of this town chant in Arabic with Arabic signs when they protest,  see: https://youtu.be/cxZXxo3Ddd8   
    
I suggest not changing the value of 'name' tag from languages to another in Areas you are not part of, and maybe stick to your town in Kalar, Kalar speak mostly Kurdish and there is no problem to use that in your town, but do not force it in Other towns my friend.       
    
Regards.    
