My daycare has a name. I don't have it registered, (maybe I should) but I was told when I was starting out that business registration was only necessary for payroll purposes. (I could use the daycare name or my name) I have never had an employee so I have never needed a business number.

(Not that this is relevant or that you asked, but when I picked a name, I chose one that wasn't strictly English. If I wanted to use only English words, I wouldn't be allowed because of the language laws. If I were to use Little Sprouts, for example, I could be fined by the language police. I would instead have to use Petites Pousses.)

Also, I discovered when I was setting up my website, Copyright applies to anything you create whether or not you register it. You register so there is proof and a paper trail, so to speak. But if you create something, it belongs to you. So if my neighbor decides she is going to use my daycare name, I can use my paperwork from 10 yrs ago with my daycare name on it and say that it is mine and claim the copyright. At least, that is my understanding.