What is the Asian national currency?
There is no Asian national currency. Asia is not a nation. It is a continent. It has many nations. Each of those nations have their own currencies.
The Turkmen new manat is the national currency of the Central Asian Turkic state of Turkmenistan. Specifically, the manat originally was introduced as the country's national currency on November 1, 1993. It replaced the Russian ruble. What now is known as the old manat was replaced by the Turkmen new manat on January 1, 2009.
I am not sure what you want to know. Before independence, British currency was used in all the colonies and was the national currency. After independence, the continental congress coined money which was a national currency. People did not fully trust the new currency and British currency was used as well.
I believe their curacy is called "yuan" (yen). "Yuan" is the official currency of Japan, but it's also the third most-traded currency in the foreign exchange market. So you can't really say that Asian money are called yen. This currency is still used only in Japan, but it is the most popular among Asian money.