Step 5. In the greeting section, select whether you want the greeting to be default or custom. Choose custom if you want to record your own voice for a personalized greeting.
Now, you will hear the Voicemail greetings instruction recorded on the phone. You will be asked to press a specific number to change the greeting. Follow the instructions and press that number.

You can change your voicemail password by calling (800)-331-0500 from your iPhone. You’ll reach AT&T’s automated customer service menu which will ask for your phone number and billing zip code. A few seconds later, the message “Password Incorrect – Enter Voicemail Password” will appear on the display of your iPhone. Enter the last seven digits of your cellphone number to change your voicemail password. I strongly recommend that you read AT&T’s support article on changing your voicemail password before attempting to do so.
How do I change my voicemail greeting on Android? Open the Phone app . Press and hold “1” to call your voicemail. Enter your PIN and press “#”. Press “*” for the menu. Press “4” to change settings. Press “1” to change your greeting. Follow the recorded instructions. Access your main voicemail menu. Listen for instructions to enter your password. From the main menu press 3 for Personal Options. Press 2 for Greetings. Press 1 to Change Greeting. Press 1 to Record personal greeting or press 2 to select the standard greeting. Tap on Call settings and select Voicemail. Tap on Voicemail service and select My carrier or My operator. Tap on Setup, select Voicemail number and type in your voicemail number. Tap on OK in the Voicemail number changed popup.