Like, say, Aaron. Or, well, Pinchas…
Well, is it permitted or not?
Yes, it is permitted, although not recommended. Unless, of course, this is a way to get closer to non-Jews and their culture.
By the way, as for that known Medrash on Jews not changing their names in Egypt, see Kotzk Blog’s analysis. (And besides, it’s meant as a symptom of the positive. This wasn’t a merit per se for which they were redeemed from exile.)