Is it proper etiquette to add the name of the person's company after the individual's name in the cc of a business letter?

Yes, it is proper etiquette to add the person's company name on a cc. In fact, the purpose of adding a cc is for the information of the recipient, if the recipient doesn't know the name, it would improper not to have the additional information. Example:

cc: Mr. Glenn Green, Sales Manager, ABC Company, Greenbrier, VT

Or if the name of the person is not available to you, the following is acceptable:

cc: Manager of Sales, ABC Company, Greenbrier, VT

Don't forget that a business letter is not only information for the recipient but it is also documentation of the information you have provided a recipient for your own records and/or your company's records.