Displaying the saved name for self-phone number in WhatsApp
Theoretically, it should. However, WhatsApp doesn't allow that. So, whilst you can still somehow start a chat with your own number and send messages, there's no way to make WhatsApp see it as a contact and show it with a name. I have tried saving it in different ways to no avail.
I often use the self chat to save important messages and to take notes without having to send the message to a random contact. And for that I just type in my number to quickly get it there.