Not that it needs re-confirmation but I phoned SVA Zurich again and this time it was a different lady and she said that they don't decide what name I can use. All they do is check to see if the forms etc are in order and then give me the official self-employed status. She said that she does not know who decides what name you can use. She spoke to her collegue and then said I should ask Handelsregister about the name. Plus she said that her collegue thinks that it needs to have my family name.
What I find sad is that some of them don't know the rules and just give out wrong info. Atleast this lady did not repeat what the other lady had said.
If it was not for Richard I would have been in deep trouble.

AbFab I did not mean for tax purposes but for initial changing of my status by SVA to independent. Anyway I don't think it will make any difference as to what company name I used on the invoice before I even was officially independent :-)