For example, an English person called Bob might introduce themselves as “Bob”, whereas an American person called Bob might introduce themselves as “Bahb”. (Sorry, don’t know the phonetic alphabet but hopefully you get my gist)
Should you pronounce those two people’s names the same, with your own natural accent, or should you copy how the person says their own name?
Edit: I specifically picked a generic English name with different pronunciation across different accents. I know my wording wasn’t great, sorry! Hopefully the edit is a bit clearer.
Context and other languages
When pronouncing a name from a different language, I firmly believe you should copy the pronunciation of the owner of that name, and not Anglicise the name unless asked to. I say this as a speaker of a language that English people regularly mispronounce and even insist to me that they know the correct pronunciation of my language.
This reminds me of the time when I met a British girl during my backpacking days in Australia. She got very upset every time anyone called her Sarah (American accent), because her name was Saaaarah (long first vowel). Everyone around her did their best to accommodate her. But it never even crossed her mind that all of us intentionally pronounced our own names in a very English friendly way, to make it easier for her as an English native speaker to address us 🤦🏻♂️
I always present myself with a pronunciation that is easier to pronounce in English. Saying my name as my mother calls me is just weird and strange when you say it in the middle of an English sentence. And likewise, I think it’s strange of people to assume that I should be using sounds that don’t exist in my native language to pronounce their name, if that is the language we’re speaking together.