And then you can tap on the "Enter a new voicemail password" option, the popup numeric keypad will appear on your screen, then you can tap in a new voicemail password. It must contain 4-7 digits.
The default voicemail greeting on the iPhone plays generic Your call has been forward to an automated voice message system recording. If you use your phone for work, create a personalized greeting that tells people you're a professional. If your phone is for personal use, create a personalized greeting so people hear your voice and know they called the right number.

How to Change the Outgoing Voicemail Message on IPhone (iOS 9 or later) Tap the phone icon (the same one you use to make a call). Tap the voicemail icon in the lower right of the screen (it’s the one that looks like an old-fashioned cassette tape). You’ll be taken to a screen that lists all of your recent voicemails; tap on the word
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.