Why is it “Midwest” and not “central”?
Because for a century it was "the West". Sometimes Illinois/Michigan/Minnesota/Wisconsin is called "the Old Northwest" (e.g. Northwestern University in Chicago).
Once there was stuff even further west, it became the Midwest (like the Mideast).
Is Texas closer to Virginia than Arizona or even California in culture?
In general, yes. Austin, San Antonio, and El Paso are more Southwestern, but the eastern 2/3 of the state are the South. The panhandle and northern bits are fairly Midwestern.
Are the Dakotas closer to California than Iowa in culture?
No, and that's why they're part of the Midwest.
Most of these maps assign Colorado, Wyoming, Montana, and Idaho to a "Mountain West" or "Rockies" region.
The problem with these maps is that the categories don't stop at state lines. Eastern OR and WA are like ID, while the western parts are more like [coastal] CA. Eastern PA is Northeastern, whereas western PA is Midwestern and the central part is basically Appalachia.