If you want to record phone calls on your smartphone, you can still do it. You just need to know a couple of tricks—or download a third-party app.
If your carrier supports the iPhone voicemail feature, you can retrieve and listen to your voicemail right from within the “Phone” app and call your contacts back by simply tapping their messages. That type of functionality is pretty neat and useful, because it saves you actual time. If not supported by your carrier, you will not be able to see the visual overview of your voicemail inbox and use any of the related features. Tapping the “Voicemail” tab in your “Phone” app will simply call the number associated with your voicemail box. So let’s get going with creating our custom voicemail greeting on iPhone! How to record your own Voicemail on iPhone Phone → Voicemail → Greeting → Custom → Record → Save

Here are step-by-step instructions: Open the Phone app. Press and Hold number 1 to call your voicemail service. You will be asked for a PIN if your voicemail is already set up. You can reset it …
Avoid background noise. Whether you have music playing in your office, or you’re sitting in a coffee shop, background noise can make it difficult for your customers to understand your greeting. Limit the noise around you when you leave your voicemail greeting.