permit of stay in Italy; writing of german surname (Rome)

Hallo all! I came to live in Rome 15 years ago. When I asked for my first permit of stay, authorities changed writing of my surname into "Gorgens" (not accepting international, or nowadays electronic writing, which is "Goergens"). I oftenly mentioned the problem and asked unsuccessfully to change it. Since last year I was more than once told that the writing of my surname in my (german) passport (!) was mistaken, and therefore the passport could be unvalid in Italy - better to ask for an italian one, with the writing of my surname as it should be, "Gorgens". German consulate told me that they were not responsible for my problems with public italian administration (Their declaration of the different types of writing of my name were not at all of interest at the anagrafe centrale, beeing issued by the German consulate and therefore not valid in Rome, ..). And the anagrafe even told me that I cannot open a (longlasting and expensive) proceedure of changing my surname, as for them sono "completamente aopposto". Is it possible that I must accept changed writing of my surname to be in order in Rome, and therefore have one surname in Rome and another one in the rest of the world, and in Internet? Or accept a new passport, with my surname written differently to all documents preceeding to my stay in Rome? Does anybody have similar experiences or proposals for solutions? Thanks to everybody, Britta Goergens