If I am self-employed, can I give my business a name?

I was reading the article by gices about how to register as self-employed, but I have a few questions, not answered:

• Can I give my business a name, if I am self-employed e.g. Pattiserie Marie or do I need to register a company name?

• What will happen, if I register as self-employed, then my turnover is over Rs2M, can I change to a company easily?

• Am I allowed to start advertising on facebook to see if there is any interest in my cakes (but take no money), before registering as self employed?

Merci beaucoup! :)