The default, generic voicemail greeting that comes with your iPhone is fine but also rather bland and boring. You can personalize the voicemail greeting on iPhone by recording your own custom version of it. This is a tutorial on how to create a custom iPhone Voicemail greeting.
2. Once there, tap on "Greeting" in the top-left corner. Your iPhone will take a few moments to fetch and load your current voicemail greeting, which you can play using the controls in the middle of the page.

Changing default voicemail to the custom greeting is very simple until iPhone won’t save custom voicemail greeting or custom voicemail greeting on iPhone not working issue arises. Don’t worry, you are not the only one with this problem, till now many users have fixed the unable to change voicemail greeting on iPhone with the help of below solutions.
We’re keeping it simple with this one. Just a few basic elements to help you get started. As long as you know who your audience is, the message you wish to convey, and the information you need from the caller, the rest should fall into place quite nicely. Let’s face it, a voicemail greeting for a lumber company will probably be different than that of a psychologist’s office. One greeting is aimed at securing potential customers, and the other is geared towards appointments, more or less. Once you are certain who your caller is, the better your voicemail. Center on your audience, first and foremost. Knowing what to relate ensures that your caller will leave the right message. For instance, if you’re a retail store, you would include your hours of operations, and perhaps any specials that you’re running. If you are a therapist’s office, then you’d need to include an alternate number in case a patient is having an issue and requires immediate help. Again, this will vary depending on the business. Here, a therapist would definitely request the caller leave their contact information. However, a retail store chain might not request that. There are also complex voicemail systems such as those used by mobile phone services, which ask you to press a certain number on your phone, where you are asked to leave your account information. Again, as you can see, it all boils down to the demographics of your callers, and what you need from them to conduct the best business possible. Depending on the situation, your caller might be in a good mood or not. In either case, they’ll probably be eagerly awaiting your call. So, it stands to reason that you only promise them a call back if you can deliver. In other words, if you’re a small shop and you’ve decided to close due to a much-needed sabbatical, then don’t leave a voicemail greeting where you promise them to call right back. However, if you have an active customer service staff, then you can promise to return their call within the same day.