Is there a phrase for someone being ashamed of, or self-conscious about their accent when moving to another region?

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 might regard their own accent with distaste and may try to imitate the accent of the elite where they live or the elite who live in great cultural centers; for example, a French-Canadian in Paris, a Brummie in London, or a Texan in Boston.

As for the answer to my question, there is one, I know. 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 now. I'm looking for a phrase describing the person or the condition.

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.

He/she felt linguistically discriminated or to be precise accentually discriminated.
The condition is called accentism.

Linguistic discrimination is the unfair treatment of an individual based solely on their use of language. This use of language may include the individual's native language or other characteristics of the person's speech, such as an accent, the size of vocabulary, and syntax.

Update:

phonetic accommodation: Phonetic imitation is the unintentional, spontaneous acquisition of speech characteristics of the interlocutor.

Novelty and social preference in phonetic accommodation
Previous work has shown that imitation is strongly moderated by social preference in adults, and that social preference affects children's speech acquisition within peer groups. linguistics.berkley.edu

(Also see. Communication accommodation theory)

Self conscious: Defined by Merriam Webster as: "uncomfortably nervous about or embarrassed by what other people think about you..." I've used the phrase in a sentence to make the phrase clearer. "She rarely spoke up in meetings because she was self-conscious about her accent."

Are you looking for Communication accomodation theory? Specifically:

convergence -

Convergence refers to the process through which an individual shifts his or her speech patterns in interaction so that they more closely resemble the speech patterns of speech partners. ...

People use convergence based on their perceptions of others, as well as what they are able to infer about them and their backgrounds. ...

Thus when an individual shifts his speech and non-verbal behaviors in order to assimilate to the other it can result in a more favorable appraisal of him, that is: when convergence is perceived positively it is likely to enhance both the conversation and the attraction between the listener and the speaker. For this reason it could be said that convergence reflects “an individual’s desire for social approval”[3] from his interlocutor, and that the greater the individual’s need for social approval, the more likely he or she is to converge.

In any event I didn't dig up an name for a converger in this sense, but I thought this might help the discussion.