Some companies are very well known—Wal-Mart, IBM, or Aetna Insurance, for example—but most are not. You will need to indicate if the company is a computer or manufacturing firm, and describe the type of computer firm (software or hardware) or products manufactured. Indicate the size of the organization, total staff, and whether it is a local, national or international firm. How this information will be received by a recruiter will depend on the position you are seeking. If you work for a local firm and it is a small office that may be very attractive to another small firm. On the other hand, a recruiter may be impressed that you have experience in a mid-size or large corporation.
If you were in charge of a division or department, indicate the size budget you handled. Especially if you are applying for financial positions—from Bookkeeper to Chief Financial Officer—the size of funds handled is a good indication of your responsibilities. Municipal budgets indicate the size of the town, city or county and are also helpful to the recruiters.