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.

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.