Squishy is in reference to the baby jellyfish that Dori, the blue fish in Finding Nemo, names.
"I shall call him Squishy and he shall be mine and he shall by my Squishy. Come here, Squishy. Come here, little Squishy. Goo Chee Goo Chee Goo. ---OW!!! Bad Squishy! Bad Squishy!" - Dori
Pat Lin Shu named Clinton Green her Squishy because she was bored one day... a day in which she saw Finding Nemo and now Clinty Boy is also named Squishy.