no, Khan is the title of ruler in Mongolic and Turkic languages which are not related to Mandarian language (a branch of Sino-Tibetan).
Han is a name of river in Southwest China. It is a tributary water of Yantze River in Southern China. The founder of Han dynasty Liu Bang received his fiefdom in the Han river vally in Southwest China (today's Sichuan province). After he defeated everyone he named his dynasty Han, a tradition of naming by ariscratical title. The population would not be named Han as there is no reason to call your own name. People would self introduce as Zhongyuan Ren (people from central plain), or Lingnan Ren (people from morden day Guangdong) and so on. Only in Yuan dynasty, the mongol emperor need a catagorization for official assignment based on the time of joining Chengis Khan's struggle, they made four catagories under their rule, and Han was used officially for the first time to refer to a population.
In short, Han is name of a river to name of a dynasty to name of people.
Interestingly in most European languages, the word like Chin, Sinea, China, Kina are the name of first dynasy before Han. But inside China the dynasty lasted for very short time, so the name did not stick around as Han would.
That is incorrect. The name Han was from 天汉, the Mikey Way Galaxy.
I don't know why people are arguing about this. Han is just a name. You could also call it Hua or Huaxia or whatever you want, really.
The true meaningful category is Sinitic speakers (speakers of historical Chinese languages), analogous to terms like "Germanic" or "Slavic" or "Japonic". But Sinitic only covers the linguistic link. It is necessary but insufficient to determine closeness.
If you look at the way the world is organized, almost always, people are organized according to
both language and race.
An English speaking East Asian in the US won't be accepted as "fully American." Even though liberals claim the US is a melting pot, in truth, race matters, these days more & more. The US's turn towards fascism and racial nationalism won't end well for people who merely speak English, but don't "look" American (= white European).
And while some Chinese (the liberals especially) would like to pretend that China is defined culturally and so anyone can be Chinese if they speak Chinese and practice Chinese culture, the reality is that it's not true. If you see a black guy in China, even if he acts exactly like a Chinese, chances are he's going to get stares and whispers wherever he goes, and will be treated as a "foreigner" at first glance - because the definition of Chinese for the vast majority of the population is "East Asian" + "Sinitic speaking." Just being the latter isn't enough.
Just the same, even though you can barely distinguish Koreans and Chinese physically, the fact that Koreans speak a completely different language (Koreanic) means they aren't truly members of the Sinitic world. They're not as close as, say, Malaysian Chinese or Singaporean Chinese or even Taiwanese. This is shown in the diaspora where Taiwanese and mainland Chinese, supposed mortal enemies, often congregate together in communities, but Koreans keep to their own.
If we want to be truly objective about how identity is defined, then we should stop basing it around how liberals
want to see the world, and instead look at how the world
actually is.