What do you call the ethnic group of people who are of English ancestry? Do you call them Anglo-Saxons?
Amusingly, at least to those non-Americans who have the pleasure of talking about this subject with Americans, the customary term in conversation is: "English".
Similarly, those of German ancestry are called "German", Korean ancestry "Korean", and Zimbabwean ancestry "Zimbabwean". As a culture of immigrants, we more or less wear our ancestry proudly and directly. It doesn't matter how many generations back it goes. Note that this is specifically for use in the US: if you are in Ireland, for example, it would be inappropriate (and potentially rude) to call yourself Irish. This is a fairly common faux pas of Americans abroad.
If you are referring to a context in which one would be expected to understand that these individuals are not, in fact, English immigrants but simply Americans of English descent or heritage, you are left with explicit constructions to that effect:
Americans of English descent/heritage are concentrated largely in the East, while those of East Asian descent/heritage are in the West
Anglo-Saxon tends to stand in for all white Americans in popular usage. At this point I would recommend being quite explicit that you mean the truly Anglo-Saxon ethnic group if you want to use that term, but it has historical meaning only and is in no sense cultural. I assume that this usage is a result of the popularity of the term "WASPs" (White Anglo-Saxon Protestants), but I don't have any hard data on that.
In the US, we have lots of ways to discuss this depending on what we're talking about:
One option is to use the term "heritage" to discuss our origin.
I'm of "Italian heritage".
We can also enumerate where we come from. The US is the "Great Melting-pot", so most people are a mix...
I'm half Italian, part British, and a little French... and there's some other random stuff in there, too.
This means that my parents are from families that came from Italy, Britain, France and a few other places.
We often use fractions if we know about what part of our family came from a particular place, and terms like "part" and "a little" if we don't know how much.
So, if someone wanted to say that they're English, they could say:
I'm of English heritage.
I'm 100% English.
My family is from England.
They could also say British, as that's generally taken to be synonymous. In some circles they might say "Anglo-Saxon"... but I don't think most people know what the term means any more, so it's easier to say the country name.
I have never called anyone an Anglo-Saxon. However, to be technical, Anglo-Saxon does mean "of English descent." But that word is rarely used. There is the term WASP, which means "White Anglo-Saxon Protestant." But this is more of a sociological term (see the definition), and by its literal definition excludes: non-whites and non-Protestants.
In the USA, as your question asks, a more common term is Anglo-American. However, as that article shows, this term can also have other meanings, therefore its usage can cause confusion and even dissension.
If you want to narrow it down, you can use: English-American. See the same wikipedia article. I do not know anybody who uses that term. Maybe some people do--probably only those who find it important to claim that they are of English descent.
British-American is problematic, because Britain encompasses more than just England.