I recognized half: Alonso, Soto, Syndergaard, Ohtani and Donaldson.
The only other ones that jump to mind among current players are Francisco Lindor as Mr. Smile, Matt Adams as Big City and Nelson Cruz as Boomstick.
I nicknamed Jesús Luzardo "the Basilisk," AKA the Jesus Lizard, but that doesn't seem to have caught on.
Matt Adams as Big City is a good one and pretty well known. Nelson Cruz as Boomstick is a good one.
You more than I did.
