OK team, let's do this. Just remember the rules - there are no rules. This list will be edited accordingly whenever a consensus is reached for a player. Let's start with a small list now so we can stay focused. Some of these are my suggestion, so obviously open for discussion.
In no particular order:
Paul Goldschmidt - Goldy / Goldzilla / Golddinger
Aaron Hill - Soup
Adam Eaton - Spanky
Didi Gregorius - The Darting Dutchman (D.D.)
Miguel Montero - Miggy / Microwave
Martin Prado - ???
A.J. Pollock - Polly
Wil Nieves - Grandmother
Patrick Corbin - The Chief
Brad Ziegler - Thumper
Wade Miley - Torgo