Also, only somewhat related, supposedly, Roddenberry had a friend in WWII named Kim Noonien Singh who he lost touch with and named Khan after him in tribute. The weird thing is that the friend was supposed to be Chinese and none of that name sounds Chinese.
It could also be a butchered understanding of their name, ex. Qin as kim, Nguyen as noonien (Whos to say they werent from down sound with Viet family), song as singh. Etc.
Add to that using the wade-giles or mathews or whatever old timey pronunciation/spelling system, the passage of time, and a bit of 1940s racism in not bothering to get foreign sounding names correct and you could easily end up at Kim Noonien Singh.
It's just hard to know whether or not it's a real story. Even if Gene himself told it (which I'm not sure if he did) as he was kind of known for embellishing stories.
I'm probably far from the first person to make this connection, but Noonien seems like a pretty obvious phonetic misspelling of Nguyen to me. I last watched TOS and a lot of material related to Khan as a kid and I don't know too much about Roddenberry as a person, but given his other stances I think it's not impossible that this is his "hidden" commentary on the Vietnam war.
And even putting all of that aside for a moment; his "friend" (if he really existed) might've been ethnically Chinese, but born in a different Southeast Asian country and the native language there then adapted his Chinese name to fit their phonology. But I don't know, I'm not a professional linguist, I might be way off here...
(Ah I just saw Deceptichum had pretty much the same thought as me but was faster in writing them down ^^')