> How did the term "Arabic numerals" come to be used for digits
> that aren't, well, Arabic?

As others explained before, Europeans got them by the Arabians.

I think that the first Europeans who started using them were mathematicians
who studied and translated Arabic mathematic books.

This is also the reason why many terms related to calculus are from Arabic:
zero (from as-sifr), algebra (from "Al-Jabr...": the first words from the
title of a famous Arabic book about calculus), algorithm (from
al-Kuwarithmi: the author of that book)...

> Is this term still being taught? Just in America or
> elsewhere? Is there a better term?

I think yes. It is the same term we normally use in, e.g., Italian ("cifre
arabe", "numeri arabi").

"Arabic numerals" sounds charming to me, and also has the advantage to
remind us that not everything was invented by Europeans.

In contexts where confusion may arise with the digits actually used in
Arabic countries, "European numerals" or "Western numerals" can go.

> Is there a traditional name for the group of digits starting
> with U+0660?

Arabians themselves call them "Hindi numbers".

This too is a charming term, because it tells us the first part of the
story: Arabians themselves got the decimal digits from a computing system
invented by Indian merchants.

But, also in this case, confusion may arise with the digits normally used in
the Devanagari script.

_ Marco