You can prevent a company from appearing in the communication log, the following video explains how to do this. There are step-by-step instructions below the video.
Steps
Open CRM.
Click on Leads (Comm Log).
Select thecompany you wish to exclude.
Click on the Grid Actionsbutton.
Select the Exclude Company from Communications Log.
Click Continue in the popup. The company will no longer appear in the Communications Log.