For example i want to register a domain and checkout with bitpay.
Could they get any details about me this way ?
I would be using a proxy through a VPS.
and for the record I am not doing anything illegal, it's just that in the future who knows if crypto activity will be. I just want to be sure.
Who is they? Your customers? The government? BitPay?
You will need to provide BitPay with contact details and payment details. If the feds ask BitPay for this information they will likely provide it.
If you want total anonymity my advice would be to avoid payment processors like the plague.