Laura I didn't mean a business, just a company say "Vanessa consulting". You keep been employed as a contractors but through your company. But instead of contract you will have a formal permanent employment, your can provide a letter of employment with company seal, etc. And everything is absolutely legal.
if I'm not completely wrong, it's the same with my father, but I would ask again.
If so, we could give @Vanessa a few tips. 😉
Laura company is a legal entity.
which legal forms do you have ? in germany are there for example GmbH , KG, AG etc. what do you have?