In business and technical writing, it is standard practice to index company names by their distinctive parts and to use full names followed by abbreviations or acronyms on first reference, with subsequent references using only the abbreviation or acronym.
The words 'The', 'Company', 'Corporation', etc. are non-distinctive filing units when they are part of the company names: index them after the more distinctive parts of the name. When composing a professional or academic report, it's important to write out full names the first time they are used, followed by any abbreviations or acronyms in parentheses. Subsequently, you can then use the abbreviation or acronym for brevity.
For instance, in technical writing, you may encounter the full name being used followed by the acronym, like 'U.S. Department of Agriculture (USDA)' or 'Occupational Safety and Health Administration (OSHA)'. After introducing the full name with the acronym, for the rest of the document, the abbreviation USDA or OSHA is used.