The reason that Time & Chaos displays columns in the contact list for both Lastname, First and Company is so you can instantly change the sorting order. Clicking on the column header (the word Company at the top of the contact list) will sort all of the displayed contacts in alphabetical order by Company Name. Clicking again on the column for Lastname, First will resort the list alphabetically by the lastname or surname of the contacts. I use the F9 key on my keyboard as a short-cut to do this many many times during a typical day.
This help article applies to Time & Chaos 7