There's no difference. Naming your company is like naming your game. It can be accurate and descriptive, or whimsical and random. And whether it contains the words studio, company, or game make no difference -- legal or otherwise.
You don't have to register your company name. But there are advantages to doing so. First, registering the name makes it easier to sue if someone else uses that name. And if you're looking for investors or partners, having a legally registered name is useful. Same for tax purposes.
Check the local and national laws where you live. Anybody can figure it out -- you don't need a lawyer. Seriously, it's easy. Just be prepared to pay whatever fees are required.
But if you're a hobbyist, or a kid, or just having fun, then don't bother registering. Just choose a name you like. Maybe get a website with that name too. And a twitter account, and facebook page with that name. (Just make sure they aren't already in use.)
Poof, you're a company.