If you still remember the password of voicemail on iPhone, you can easily change the password of your voicemail on iPhone. When you forget the voicemail password, you should retrieve the information from the Email or call the carrier directly for a solution.
However, some cellular service providers allow users to access and update their voicemail by calling their own numbers from working landlines or phones on other wireless networks, so users whose accounts include such an option and who have access to alternative service could keep the voicemail greetings updated even when their own mobile phones cannot connect to cellular or internet service.

You will be asked to delete your current Voicemail greeting. Click on the ‘Yes’ button that appears on the screen if you want to remove that. You can save your new recorded Voicemail greeting or can use the default recorded option. Wait and hear the new Voicemail greeting message that the instructions speak out. If you want to keep that recording as your Voicemail greeting, then save it. Or you can re-record the message to get a different greeting.
If you don't record a new greeting, callers hear the default greeting. To record a new greeting: Open the Google Voice app . At the top left, tap Menu Settings. In the Voicemail section, tap Voicemail greeting. Tap Record a greeting. Tap Record . Record your greeting and when you’re done, tap Stop . Choose what you want to do with the recording: