Hello,
Not sure if this is a school related question but i have the answer for ya (:
There are multiple reasons on why you shouldn't let another person use your business name.
1. They can make YOUR profit off of what you sell
2. It can lead to a law suit in the future
3. 2 businesses using the same name always leads to unwanted problems, finance cases, business claims, and the possibility of being sued by the other person.
Best option would be for you to make your own business name and get it trademarked so that nobody will copy you! (:
