I asked myself the same question when getting US citizenship (also born Polish). Ended up not changing my name (although in English few letters aren't exact, like using L instead of Ł). I don't mind showing my ID, but just like you, people still manage to mess it up. It often ends up being a starter to interesting conversations, which personally I've enjoyed. Having a real unique name can have an advantage - I've never received a bill that wasn't actually for me, unlike my American friends with common first name/last name combinations.
I have a family plan, they just raised the price of the subscription in October of last year from $14.99 to $17.99... I was already thinking that's too much, but now I'm definitely done with them.
Even with VPN, ultimately you're still storing everything at your house. Seedbox, preferably in the Netherlands is the way to go.