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.
The process is very simple. You'll just have to click the green phone icon, the same place you make calls, and navigate to the voicemail screen. On the voicemail screen, you'll see a greetings option on the top left.

Website: https://masd.happyfox.com/kb/article/16-how-do-i-change-my-voicemail-greeting-message/
If you don’t make any changes the default iPhone voicemail message is pretty bland and not very professional. It is a good idea to change the iPhone voicemail message to something more professional or at least something that lets callers know they reached the right person.