Today lecture is the rules for company’s name. The is only one rule that you need to put the types of your company at the beginning or at the end.
For example, in case you stablish Kabushiki Kaisha(株式会社), you company name must be either XXX株式会社 or 株式会社XXX.

If you establish Godo Kaisha(合同会社), your company’s name will be either XXX合同会社or XXX合同会社

By the way, you can register the same name as other companies as long as the address of the companies are different.
However, do not use the name of famous companies because they might sue you if their brand name is violated.