I think this is not so much a linguistic question but rather a matter of law. Each state (and each federal state in USA) has its own rules on how the "business name" of the company should be created. Usually there is a part created by its author (e.g. The Correct Grammar Company) and the additive created by the law (e.g. Inc., Co., Ltd., LLP, LLC and so on). Its purpose it to infrom the general public about the legal form of company, because each type for example guarantees a different level of settling the debts of the company. For this reason it is necessary to add these additives to the name of the company. I don't know how it is in USA but in Slovakia, and generally in EU, there is a statutory obligation of the company to use this additive in every occasion, in all business documents and contracts. In Slovakia, there is also a duty to separate the created part of the name from its statutory part by a comma. Its purpose is to clearly show what is the form of the company. Nevertheless, I have to say that companies sometimes ignore this duty, but it's mainly because of their distraction and not their intention.
Companies which do not use their legal additive do it in two forms:
1. in their trade marks - mostly accompanied with their logos or graphical symbols, this is not their legal "business name", it's just their identification and it's mainly used on websites
2. in their business names - in official documents like contracts used as an identification of the company (usually connected with its registered office and identification number), In this case they are obliged to write the statutory additive because it is a full description of this company.
Is this answer accurate enough?