iOS 7's new design seemed to cause some spacing issues in Messages, especially on the iPhone. Where you formerly could see the full names of the people you texted, iOS 7 shows only a first name, or perhaps a first name and last initial. When you know as many Dans as I do—even as many Dan M.'s as I do—that just won't do.
There's a fix, though the setting isn't where you might expect.
In the Settings app, tap on Mail, Contacts, Calendars. and then scroll way down to the Contacts section. Under that header, tap on Short Name. For my purposes, I turned off both Short Name and Prefer Nicknames. Now, Messages shows the full names of the contacts I'm sending messages to, shortening the button labels at the top as necessary to make everything fit.
Mac OS X Hints