The permission that is required to merge companies/contacts under Admin/Manage Users/User Modify/Companies – ‘Can merge duplicate companies and their contacts’ as per the below example:

In the above example, there are some duplicate contacts - If you select the Merge button you will get a screen that will allow you to select duplicate contacts as follows:

Confirm that this is the contact you wish to Merge and click the OK button:

By pressing the Merge button, you’ll see that duplicate contacts have been disabled (in red) as below: