In an effort to make iOS 7 more simple and clean, Apple decided to make the Messages app only show a person's first name. Unfortunately, I have sent messages to the wrong person because I know many Davids, Tommys, and Marks. You are, however, provided an option to always show a person's full name.Visit the Settings app > Mail, Contacts, Calendars > Short Name (in the Contacts section). Turn off Short Name and Probably "Prefer Nicknames". If you leave Nicknames on, you will not see their last name, either.
Force Messages to show full names so you don't accidentally text the wrong person