>WhatsApp on Android has the same behaviour. Most of my conversations show as a bare phone number because I decided not to give it all my contacts.
It was actually worse (at least as of a few years ago) because they didn't allow you to manually input phone numbers. You either need the other party to message you first, or use a wa.me deeplink (eg. wa.me/12125551234).
I would have settled for something like the Instagram “iPad app”: a phone-sized rectangle in the middle of a black background. Alas, they don’t even allow that, hence all the fake crap you can easily download by mistake. And the web app is pretty bad on iPads, thanks in no small part to Apple.
However, WhatsApp groups show a name, so that's a workaround if you are using WhatsApp with someone you know well: Make a group for the two of you.
When a friend went to install WhatsApp for their iPad, they succeeded!
Then they said it wasn't working properly. Unfortunately that's because app store search brought up misleading third-party WhatsApp apps for the iPad. If you weren't paying attention, it was too easy to think you were installing the official app from WhatsApp. I didn't notice the app was third-party at first either, and I was very surprised to find no app at all from WhatsApp itself on closer inspection, amidst a page of search resulrs all claiming to be it.