The Google app is now rumored to add a feature called "Personal Speech Recognition" in the course of a future update. It is slated to help the OEM's Assistant to respond better to words or names uttered most frequently by the user - however, this requires that the same user allows the AI to record their voice on their device.
https://www.notebookcheck.net/Google-Assistant-is-slated-to-update-to-the-ability-to-record-a-user-s-voice-to-learn-more-about-it-in-the-future.623345.0.html