Nice to meet you, I am Matthew Zhang

>Nice to meet you, I am Matthew Zhang.
Does this happen in your country?

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No

Nice to meet you Matthew-san

yes
a guy I believed a westerner turned out to be Chinese from mainland when I met him
there was no Chinese name in his emails

Why do they have names like Jason Chen, Winston Wang? Like why the first name isn't Chinese?

Because they got bleached

White people cannot into Chinese names.

Western influence, same reason why we have names like "Kabir", "Jamal", "Khalid" etc. even if we aren't Persian or Arab.

Indian people have those sort of names? Even the non-Muslim ones?

yes
they take traditional french name and keep their ching chong last name