Ok. Now I know why it does not create ticket. 
I try to manually create a ticket as a client, and this is the error message I received. 
  
  
SQLSTATE[HY000]: General error: 1364 Field 'name' doesn't have a default value on line 124 in /var/www/******/customer/lib/model.php 
  
  
So, what's this problem? First time seeing this.