Your find is showing all of the contacts related to the company because you are searching from the perspective of the Company table. While residing on the Company layout, you are essentially asking "What COMPANIES have a contact with this person's name?"
To get what you want, you would need to ask "What CONTACT has this name, and what company is he associated with?" To do this, do your find from a layout based on the Contacts table. Perhaps have a find layout, based on contacts, that also shows the related company info...it could closely resemble your current company layout, but the layout itself should be based on the Contact Table.