A user cannot be created without the Name property specified. For users, the value of the Name property always equals to Full Name. If you removed the Full Name property from the user creation form together with the properties it consists of (by default, First Name and Last Name), you will not be able to create users.
As a workaround, you can add the property to your Home Page Action as a predefined field.
For instructions on how to do this, see Step 4 under Create New Object in Configure Home Page Actions.