Step 1 – Set your PIN – this protects your mailbox from eavesdroppers. Log on to your mailbox. Dial 6 7 for mailbox options. Dial 7 for security code. The phone system will guide you through replacing your 4-digit security code. Step 2 – Record your name. Callers may hear your recorded name before leaving you a message.
If your carrier supports the iPhone voicemail feature, you can retrieve and listen to your voicemail right from within the “Phone” app and call your contacts back by simply tapping their messages. That type of functionality is pretty neat and useful, because it saves you actual time. If not supported by your carrier, you will not be able to see the visual overview of your voicemail inbox and use any of the related features. Tapping the “Voicemail” tab in your “Phone” app will simply call the number associated with your voicemail box. So let’s get going with creating our custom voicemail greeting on iPhone! How to record your own Voicemail on iPhone Phone → Voicemail → Greeting → Custom → Record → Save

Step 3. You will be asked to create a voicemail password. Create a password and then tap “Done”
No you can’t. I just called and asked for it to be turned off completely and was told it is impossible. It’s aggravating to get conflicting information. Obviously either the CS Team member who wrote the previous post, or the employee I just spoke to on the phone, doesn’t know what they’re talking about.