With travel as it is now, and possibly even more in future years, I'd expect almost everyone on Earth to be of "mixed race" by the 23rd century. She reminds me, a little, of Indira Ghandi. If she wasn't meant to be Indian I'd be surprised, and it's too bad too because for being the two most populated countries there aren't many Chinese or Indian characters in any Star Trek.
There are a few, mostly in small roles, but African characters massively outgun tthem as Trek progresses in terms of screen time.
I have three possible explanations for the relative lack if Chinese or Indian characters in
Star Trek.
ONE:
In "Space Seed" Khan is identified as:
KIRK: Name, Khan, as we know him today. (Spock changes the picture) Name, Khan Noonien Singh.
SPOCK: From 1992 through 1996, absolute ruler of more than a quarter of your world. From Asia through the Middle East.
MCCOY: The last of the tyrants to be overthrown.
Other supermen later gained power in other countries:
SPOCK: There is that possibility, Captain. His age would be correct. In 1993, a group of these young supermen did seize power simultaneously in over forty nations.
KIRK: Well, they were hardly supermen. They were aggressive, arrogant. They began to battle among themselves.
The wars between the countries ruled by the supermen may have been very violent:
Whole populations were being bombed out of existence.
Was China ruled by one of the supermen who might have been an opponent of Khan in the Eugenics Wars? Maybe:
"Patterns of Force":
SPOCK: Yes. Earthmen like Ramses, Alexander, Caesar, Napoleon, Hitler, Lee Kuan. Your whole Earth history is made up of men seeking absolute power.
"Whom Gods Destroy":
GARTH: On your knees before me! All the others before me have failed. Alexander, Caesar, Napoleon, Hitler, Lee Kuan, Krotus! All of them are dust! But I will triumph! I will make the ultimate conquest!
It is possible that Lee Kuan was a superman who ruled China and fought an atomic war with Khan Noonian Singh.
Thus China and India might possibly have suffered the most in those bombings, presumably carried out by ICBMs. And possibly the radioactive fallout and/or chemical and/or biological weapons, may have caused mass sterility and caused the populations of East Asia and South Asia to plummet for decades, generations, or even centuries after the war.
TWO:
For some unknown sociological reasons, the populations of East Asia and South Asia in the
Star Trek future might not be as adventurous or interested in space exploration as the populations of other regions of Earth, despite the fact that some regions in East Asia and South Asia had seafaring traditions for thousands of years.
If that is the case, it may result in most of the Earth people who move to colony planets not being East Asian or South Asian. And if possibly a large proportion of Starfleet is recruited from Earth colonists on distant planets, most of those colonial recruits to Starfleet would not be of East Asian or South Asian ancestry.
THREE:
Many planets in TOS have natives who look totally like Earth Humans despite the fact that there is no evidence that those planets were settled by Earth Humans after Earth discovered faster than light interstellar travel a little more than 200 years before TOS. In fact the
Enterprise is sometimes the first Earth or Federation ship known to have visited such a planet.
So those human-looking natives seem at first sight to have originated on those planets by convergent evolution. In science fiction aliens who walk on two legs and have two arms and a head on top of their torsos are said to be humanoid. Andorians, Tellarites, Klingons, and Gorns are all humanoid. But in
Star Trek the word humanoid seems to mean looking exactly like Earth Humans, though I call those aliens who look like Earth Humans exo-Humans..
In "The Paradise Syndrome" Earth plants are found on a distant planet, as well as people who look like American Indians. Later Spock studies the symbols found on a strange obelisk on the planet:
SPOCK: Yes. The obelisk is a marker, just as I thought. It was left by a super-race known as the Preservers. They passed through the galaxy rescuing primitive cultures which were in danger of extinction and seeding them, so to speak, where they could live and grow.
MCCOY: I've always wondered why there were so many humanoids scattered through the galaxy.
SPOCK: So have I. Apparently the Preservers account for a number of them.
Thus it is possible that many or most of those humanoids or exo-Humans found on alien planets may be descended from Earth Humans brought to those planets by the Preservers.
Most of those humanoids or exo-Humans look like "white" or "Caucasian" or "European" Humans, no doubt because the majority of available actors in Los Angeles are more or less "white" or "Caucasian" or "European". So it is possible that for some unspecified reason the Preservers mostly took "white" or "Caucasian" or "European" people from Earth to seed on alien planets.
And if exo-Humans who look "white" or "Caucasian" or "European". are very common, there should be many planets with such exo-Humans in the Federation. So it is possible that a lot of the Federation citizens and Starfleet members seen are actually exo-Humans who look like Earth Humans, and look like "white" or "Caucasian" or "European" ones at that.
If the Preservers settled members of European cultures on alien planets, those transplanted people would probably retain their European cultures and languages and names at the times they were contracted and joined the Federation. Thus having a name in an Earth language need not prove that a
Star Trek character is descended from Earth Humans and is not actually an exo-human descended from Earth Humans brought to his planet by the Preservers.
And if Earth is very important in the Federation, it may be common for exo-Humans to take Earth names. In E.E. Smith's
Lensman series some aliens used Earth names. I remember a crime lord named Edmund Crowninshield, for example, and he didn't even look English, being a blue skinned Kalonian.
CONCLUSION:
So it is possible that some combination of the those three possibilities - and maybe others I didn't think of - is the in universe cause of the relative lack of East Asian and South Asian characters in various
Star Trek productions.