That is really interesting. I was in a similar situation, but I refused to change my impossible to pronounce by an US-er name. The main reason was that many immigrants did that and I found that in a poor taste. A guy who speaks with a thick foreign accent named Bob Smith? Give me a break. So I got stuck with my old world name and have to go through the daily ritual of "You do you spell/pronounce that?"
I think names are a part of a person's cultural heritage but certainly NOT a part of identity politics. I was named by my parents in a way that I do not particularly like, but I grew up with that name and that became a part of my heritage. Changing that to conform to the rules of identity politics, as many celebrities and religious/ideological converts do, is in my book a form of "ostrich idealism" - the "I cannot change the material conditions of my existence, but I can assume a new name and change the style of my clothing to become a 'new person' that way" self-defeating rationalization.
Wojtek