The very first thing to be checked is, have you set up the voicemail earlier or directly recording the voicemail greeting? If you haven’t already set up the voicemail and unable to record voicemail greeting, then go to the top of the page and learn how to set up voicemail on the iPhone.
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In many cases, an update to your carrier’s voicemail app or settings can resolve the issue, but don’t forget to call your voicemail number to check if it is set up correctly. Once you’ve set up your voicemail, you’re free to switch off when you need to. There are other ways you can stay in contact, however.
6. Access your greeting or recorded name settings. Next, press the key on the dial pad that corresponds to options for your greeting or recorded name. In this case, it's 3.