Interesting question. My impression from afar (I live in Japan) is that “Asian Indians” and “East Indians” are both used but that just “Indians” is increasingly common, partly because of the growth in the number of people in the U.S. from India and partly because of the growing tendency in recent decades to avoid using “Indian” to refer to native Americans. Wikipedia has a long article on the latter issue:

https://en.wikipedia.org/wiki/Native_American_name_controver...