"Inc." is a word added to the end of a company name. It stands for "incorporated" which means that the business is a corporation. In other words, it's not a business owned by a single person or a small partnership.
"Inc." is often included in the official name of a company, but may or may not be part of the commonly used brand name of the company. For example, the computer company Apple is usually just called "Apple" even though the official company name is "Apple Inc." You would say or write "Apple Inc." if you wanted to make it clear that you are talking about the company and not a piece of fruit or the products that Apple sells. So you might read this in a newspaper article:
Shares of Apple Inc. took a steep dive in trading yesterday afternoon.