You can use Hotword Changer to access your Assistant (Your default assist app or whatever opens when you long-press the home button) with different hotwords.

Hotword Changer lets you use voice wake-up feature even when the screen is turned off.

By default Hotword Changer will recognize you when you say like "Jarvis" etc. whenever the screen is on or your device is charging.

However you can run it when the screen is off but comes at the cost of increased battery usage!
(Not recommended)

There are only four hotwords available right now but support for custom hotword will be available soon.

Note:
*Simultaneous recording in apps is not allowed for third-party apps on Android (except Android 10). Hotword Changer makes this possible using a lot of hacks. Some features may or may not work.
*Feedbacks are appreciated.
*Devices not respecting "Android Foreground Services" will kill the app in the background. Check the OEMs website for possible solutions.