There are two languages whose name in MediaWiki is similar to "Kurdi": one with the code ku and the other with the code ckb.
ckb is all in the Arabic script. According to ISO 639, it's Sorani Kurdish (کوردی سۆرانی), but its name in MediaWiki is just "کوردی", which is pronounced "Kurdi" and means just "Kurdish".
ku is written in the Latin alphabet by default, and most of the content in the Wikipedia in this language is written in the Latin alphabet, but it also has script conversion to Arabic. When it's written in Latin, it's called "kurdî" or "kurdî (latînî)", and when it's written in Arabic, it's called "کوردی (عەرەبی)", which means "Kurdish (Arabic)". The first word here is the same as the name of ckb. If I understand correctly, this language is actually Kurmanji, which has its own code kmr, while ku is a macro code for all Kurdish varieties. According to Ethnologue, the name of this language in itself is "Kurdî-Kurmancî" or "Kurmancî".
There is also the language with the code sdh. There is no full-fledged Wikipedia in it, but only an Incubator. It is, however, already supported in MediaWiki, and it has the name "کوردی خوارگ"—the first word here is "Kurdi", and the second is unique to this language, so there is no ambiguity with it.
This is my understanding of facts till now. If I am incorrect about anything, please correct me.
Now, I'd like to make a careful suggestion: can ku and ckb be renamed from just "Kurdi" (in different alphabets) to a name that makes them clearly unambiguos? The most sensible thing to me is to call ckb "کوردی سۆرانی" and to call ku "Kurdî-Kurmancî" or maybe ""Kurdî Kurmancî", whatever is more correct in terms of this language's standard punctuation. I think that this is sensible because it clearly shows that both of them are Kurdish, but includes another word that helps people distinguish them clearly, without possible confusion. This will also make the consistent with the name of sdh, which begins with the word "Kurdi" and continues with a unique name.
(We should probably also change the code of ku to kmr, but for technical reasons, it's much more complicated, so it will have to be discussed separately.)
However, I don't actually know these languages. I am only raising this because I am trying to maintain the lists of languages in MediaWiki in good order, and to help users of Wikipedia and other sites that run on MediaWiki use them conveniently. Two languages with very similar names may make this inconvenient, so I'm suggesting to make them less ambiguous.
I would love to hear the opinions of the Kurdish-speaking wiki editors about this.
Thank you!