"Like a thief" is "furtim", and I honestly don't see how it could possibly become a surname! If there's Latin influence on names where you come from, then the word for good luck, which is "fortuna", is much more likely (and close to Furtuna). I think we've got the answer there!
You signed yourself Hakan Furtun. Do you use the name Idris? I have always thought it one of the finest names in any language.