I was reading a book about accents at a local library and there was a chapter where the author says "some varieties of a language are more aesthetically pleasing than others". Some accents are considered “tops”, and these are the ones spoken by the Royals, the Elite, intellectuals and Distinguished Academics, etc
Consequently, a person moving from a rural state to a megalopolis might regard their own accent with distaste and may try to imitate the accent of the locals; for example, a French-Canadian in Paris, a Brummie in London, or a Texan in Boston.
As for the answer, it's a phrase, with 3 or 4 words, and no foreign terms. It is mentioned in the book on sociolinguistics and accents I was reading. I simply can't remember it. I'm looking for a phrase describing the condition, not the person.
For Clarity: I'm not saying that all French-Canadians, Brummies or Texans are, or should ever be, ashamed/embarrassed/self-conscious of their accents, but it is possible.