You cannot install two copies of the same app on an iDevice.
Each app has an identifier that is typically (but doesn't have to be) in the form of a reverse domain-name. For example:
com.example.awesomegame
This actually gets prepended with an Apple-generated identifier unique to each publisher (or developer, if developer build). iOS will not install a duplicate copy with the same identifier.
You could do what you want if you are willing and able to use Signal instead of Whatsapp, and are a developer or willing to open a developer account. (Actually, I think there is some free option that is only a bit of a hassle signing because certificates expire after a week. I'm a developer, so not completely familiar with what your options are to avoid paying $99/year).
Build Signal from source with Xcode, and either install one from the App Store and one that you build yourself, or else install two that you build yourself, and give them different identifiers. In either case, the apps won't have the same identifiers.
As a developer, I do this all the time. (Not with Signal, but with my own apps!) I have one copy of our App Store app, and one or more under test, each using a different identifier. Makes it easy to compare the behavior of current production and versions under development or test.
If you use Signal, you also could have the option to run your own private server.
I don't know why anybody uses Whatsapp. I guess because it is popular. I hope people don't use it with the mistaken impression that it is very private.
Honestly, you might be better served by an Android device. See here:
https://www.android.com/enterprise/employees/