Use the internal Twitter search (or other means, such as Google) to search for official company Twitter accounts and put the Twitter handles in a spreadsheet (e.g. @3M, @Google, @autozone).
The spreadsheet containing company names (see attached) also has a direct link to the Twitter people search, with the company name embedded, but you aren't restricted to searching that way.
There are 5,343 company names that need to be searched. Some companies may have multiple Twitter accounts, but the majority of companies have zero or one. The first few on the spreadsheet have been done as an example.