In longer documents, especially legal and other formal documents, it is common to used defined terms. These are single words or phrases that stand in for longer terms or phrases. The most common way to do this is to use the full name and follow it by the defined term in parentheses and quotes:
This report about the Acme Company ("Company") will ...
In formal legal documents, the parentheses sometimes reads (hereinafter "Company"). Fairly wordy and pedantic. Omitting the hereinafter would rarely leave anyone in doubt about what the parentheses mean.
In many cases, a company name includes the word Company. It is very common to use the term Company to stand in for the Acme Company. It is, in effect, a defined term, whether or not a formal defining process is used.
In this case, the term Company is really part of a proper noun, and should be capitalized throughout. Even if the word company is not a part of the business name, capitalizing company avoids confusion since there are many companies, and a long report may refer to other companies. Capitalization of Company makes sure that the reader is clear about which company is being discussed at a given point in the report.
Acme Inc. is the leading purveyor of coyote deterrent material. The Company is poised to expand it goods and services to roadrunner support items.