Make Full Name field required on signup form

Hello,

Currently the “full name” in the registration form is not required. The problem is that if the user does not fill out this field, he can signup but then later he cannot access his author page.

How can I make this “full name” field required in the registration?
– OR –
How could I hide this “full name” field from the registration form and then use a hook to add the nickname and display_name programatically? What hook would it be?

This my registration page:
https://www.oigente.com/gd-login/?signup=1

QUESTION: How can I access all the questions I have ever asked in the forum of wpgeodirectory? I have open many threads but now it is hard to find them.

Thank you!