Your iPhone does have a voicemail password, but you only have to enter it once and many new iPhones set it up automatically. However, there still needs to be some form of authentication between your carrier and your iPhone to download your voicemails. Even though you don’t see it, your voicemail password still exists.
If you forget your voicemail password, you will not likely to reset it from your iPhone. You need to contact your carrier to reset your password.

With this method, you don’t need a third-party app. Call the person you want to chat with, then tap the “Add Call” button on your phone’s screen. Dial your own phone number—the one you’re calling from. This will take you to your voicemail. Once your voicemail has started recording, tap the “Merge Calls” button on your screen. Now, you’ll record your phone conversation onto a voicemail message. When you’re done with the call, you can tap the share button to export it to your Mac via Airdrop, to the Voice Memos app, or transfer it via email or text message. The file is recorded as an M4A, so depending on what you want to do with it, you may need to convert it to MP3 before uploading it to other apps.
Generally, people that call and leave messages are more likely to be ideal customers of your business. Your voicemail message is often not much more than a formality to the person calling.