Can you record conversation while on phone?

There are third party apps in the App Store that are offered by companies that offer recording services via three way calling systems (the recording service is the third party on the call). You cannot record directly on the iPhone as those services and their apps record the conversation on their servers, which you access through your account with them. All such services and their apps in the USA also announce the call is being recorded, to comply with State laws, and some will require those in the call to acknowledge that announcement.

Not using a native app, since in many countries that activity is NOT allowed.

You can search for a 3rd party app on AppStore.

Regards

Giulio