boy name opinion

Mel
Hi everyone,
My hubs and I are going with his family name William Gordon Byers IV for our rainbow baby....we planned on naming our first son that but always referred to his nickname Liam which is short for William. Liam is even on his birth certificate.
My hubs is called William
My father in law is bill
And his father goes by Gord
I want somthing differnt and special for the nickname of this rainbow baby....I have agreed with my hubby that his official name will be William Gordon byers IV but for a nickname I really like the name Willis...its unconventional and usally a surname...but I am having a hard time finding nicknames for William. What are some opinions? Is Willis a good nickname?