About registering the name of an animation production studio and comic publishing company

Hi. This is serious. I took a course called "Intellectual Property And The Law", which covered info on trademarks, copyrights and patents when I was in art school but it has been years since I have kept up with this stuff.

I am not an expert on the business and legality of intellectual properties.

From https://www.nerdwallet.com/article/small-business/trademark-vs-copyright#:~:text=Copyright%20protects%20original%20work%2C%20whereas,in%20the%20course%20of%20business :

" Copyright protects original work, whereas a trademark protects items that distinguish or identify a particular business from another. Copyright is generated automatically upon the creation of original work, whereas a trademark is established through common use of a mark in the course of business "

From https://www.dictionary.com/browse/patent :

A patent is "the exclusive right granted by a government to an inventor to manufacture, use, or sell an invention for a certain number of years. an invention or process protected by this right. an official document conferring such a right; letters patent."

I want to register the names of my own animation production studio and my own comics publishing company. Do I register for PATENTS for these company names?

How do I register the names of these two companies?

Please help. Thank you.