On your desktop you can set preference to show a company instead of person. The problem is that the company name appears on your iPhone and nothing else. You have to open the contact of each person at the company to see the individual. The two best options to fix this are to lave your desktop contacts set to show the contacts name and:
- Create a group for each company on your desktop and make sure that group is synced to your iPhone. Press the Group button on the top left of your iPhone to filter and view only the contacts for that company.
- Include the company name in the first name field: "ATT Mike". Provided you have your iPhone set to sort by first name you'll get "ATT Mike Smith". This puts all your ATT contacts together under "A". If you prefer last name, just include the company name at the start of the last name field instead and go to Home>Settings>Sort Order>Last, First.