How to make texts say new message on lock screen instead of saying the contact name iPhone 4s?

How to make texts say "new message" on lock screen instead of saying the contact name iPhone 4s?

Change the name of your contact to "new message" and don't forget who that refers to. No going around the iPhone settings.

For iOS 7:
Settings
Notification center
Messages
Show preview: off

You can also turn off the swipe down menu (notifications).

Al is right. If you still want a 'preview' but don't want a name listed, you'll have to change the names of the contacts. BUT. There's a trick you can use. 4s still allows for push notifications from Gmail and contacts. IF you use Google contacts, there's a subtitle field underneath the contact name. You can assign a 'nickname' or 'psuedo-name' there and the 4s will pick up on it. For example, my sister's name has 'Sissy' tagged to it. So all her texts and emails to me use 'Sissy' and not the contact name I have listed. Best luck.