iOS 7 contains two new options for managing contacts: blocked contacts and short names.
Blocking a contact will prevent that contact from calling, messaging, or FaceTiming you. Blocked contacts can be added in two ways: You can do it from a message by tapping the Contact text in the upper-right corner, and then tapping the (i). From Phone or from FaceTime in the Recents list, tap the (i) icon next to the contact.
After tapping the (i), scroll down to Block Caller. Tap this, read the warning text, and then tap Block Contact. This will block the contact. They don't inherently have to be in your contacts list, you just have to have received a message or call from the number or email address in order to add them to your list.
You can manage your blocked contacts not in the Mail, Contacts, and Calendars section, but from any of the Phone, Messages, or FaceTime sections in Settings.
You can remove blocked contacts from this section, and add new contacts to the list from contacts already in your book.
For the blocked contact, their iMessages will show as delivered, but will not pop up on your device. FaceTime calls will ring on their device, but not on yours. Same with phone calls - your device just pretends that they don't exist.
Now, for the people that you do want to hear from, one of the new contact options in iOS 7 is the Short Name option. This controls the way that contact names are displayed in apps like Messages. It allows for names to be displayed in a brief way, as opposed to just displaying the whole name entirely.
You can configure Short Name by going to Settings and Mail, Contacts, Calendars. The Short Name icon is under the Contacts header. By default,Short Name is set to display just the first name only, and to prefer nicknames for contacts. The settings are all fairly self-explanatory: having First Name & Last Initial will show my short name as Carter D, for example.
These features should help you manage your contacts in a much better way and make sure the people you don't want to hear from are ignored, and the people you do are shown in the way you want!