You can choose whether fields on your Contact Forms are mandatory or not.
If a field is mandatory, it means that while creating a Contact using that Contact Form, the mandatory field(s) must be completed. If they are not completed, you will be unable to press save.
Watch the walkthrough
https://www.loom.com/share/c2ee879fdc4c4070bfae6429f8f5bdeb
Steps
Go to the Edit Contact Form page of the Contact Form that you want to set fields as mandatory within
Select My Apps in top menu
Scroll across and select Contact Forms
Press the cog icon next to the Contact Form you want to edit
You arrive on the Edit Contact Form page
Tick the Mandatory tickbox shown below the name of the field
The Name field is always set as mandatory
Scroll to the bottom and press save