It seems there is some confusion here about my question let me try to be more clear.

If I use the Tor browser or serf of some coffee shops free wifi or whatever so the IP is not at all traceable back to me and make a payment to someone that has no idea who I am, and I do not give any personal information at all, and I make the payment using bitcoin, is there any way to trace out my legal identity only using the information from the bitcoin payment?