I agree at one level with your conclusion. In the end, as you say, your name should be something you are happy with. But also, since your name identifies you in several different ways, if you are going to change your name, make sure your name communicates what you want people to think before they meet you.
Also, keep in mind, you name also impacts your signature. Many years ago, as CEO of a large company, I had to sign my name 1300 times in an afternoon as part of a refinancing process involving almost a dozen lenders and more than a dozen subsidiaries. I remember thinking at the time, I need to change my name to something shorter like John Smith.
My wife is from Indonesia, when she married me, she traded an impossible name for most Americans to say to a name most Americans pronounce wrong and can't spell. But she solved that, she uses only her first name as her signature and its unique enough (her name), that unlike my first name, it identifies who she is.
America is a diverse country comprised of people of all religions, races, ethnicities, cultures, and traditions. A name is often used by others to estimate where you are individually with respect to the "American melting pot".
Some employers try to screen out people, who appear less assimilated. One of the greatest challenges in corporate America is achieving diversity without sacrificing unity. This is far more difficult than it sounds.
When someone adopts an American name, I think subconsciously or consciously they are communicating they just want to be treated as "an American". They won't get easily offended if you don't understand their religion, culture, values, beliefs, ethnicity, or race. Just treat them the same as anybody else.
I am not condoning this, but it is "a truth". I laugh when my grandson gets announced. His name is Otto Schundler... what image popped into your mind? A German kid, right? Otto is 50% African and less than 25% German; the rest is a mix. But my son loved my father and that love translated into him naming his son after my father.
Hopefully, no one will hold his name against him.