The one outlier you can't control here is the peer you trade with, but there are a couple ways to get around this, ex. Revolut's MITM payment link method.
Can you expand on Revolut payment link method, should I use payment links to both send and receive, instead of paying/receiving directly? Is it more private?
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Where does this work how you describe (where the peer does not get to know anything about you)?
I'm in the EU, I created a payment request link, then visited it and Revolut's website shows my name and surname initial along with the requested amount.
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