A new greeting can be recorded under the Greetings & Pin section of the app by first pressing the default greeting and then recording a new one.
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. How do I change my voicemail message? From the Home screen, tap the Phone icon . Tap Voicemail then tap Greeting (upper-left). Greeting is located in the top-left corner of screen. Tap Custom to record a greeting. Enabled when a checkmark is present. Tap Record to begin recording the custom greeting message. Tap Stop to end recording then tap Save. Call *86 (*VM) from the handset or the 10-digit mobile number from another phone. Follow the instructions for choosing the language options then press the # key to confirm the choice. When prompted, enter the 4-7digit password then press the # key. When prompted, say the signature (or name) then press the # key. Open your Android’s Phone app. It usually looks like a phone receiver at the bottom of the home screen. Press and hold the 1 key on the keypad. Tap Add number. Tap Service. Tap My carrier. Tap Setup. Tap Voicemail number. Type your mobile phone number and tap OK.

Setting up a new voicemail message is the same on any iPhone that runs iOS 9 or higher. Use the steps below to set a custom iPhone voicemail message.
If the you haven't changed your personal greeting, a default system greeting will be played for callers. For example, "Please leave a message for John Smith. After the tone, please record your message. When you finish recording hang-up or press the pound key for more options."