I have Lumia930 (WP8.1). I change the profile picture and name of some contacts but after some days I connected to Internet via Wi-Fi the contact's name and profile picture are return to the previous state. How can I disable this feature?
You can't prevent your contacts from being synced with your Microsoft Account unless you have a different E-Mail Account set up with which your contacts are being associated.
I would recommend to activate your Wifi when editing the contact information so these changes will be saved correctly. You can check this by signing in to outlook.com with you Microsoft Account (and also make edits there).