"Fridge" is a shortening of the word "Frigidaire", which is a brand of appliances. Back in the day, "Frigidaire" became a bit of a generic term, for refrigerators (like "Kleenex" and "Kitty Litter") and was subsequently shortened to "fridge".
As for "Fanny", it can also be the diminutive of "Frances" i.e.: "Fanny Hill" or the author/comedienne Fanny Flagg.
As for "Fanny" ... one of my most memorable high school teachers (and the feistiest woman you'll ever meet) was given the name Fanny at birth. As an adult, esp. becoming a high school teacher, she hated her name and had it legally changed to Fanne with an accent over the 'e', thus the pronunciation became 'Fan-nay.'
I failed her class (history), but she helped me through some rough patches outside of class... she's an amazing woman... a bit ditzy, but amazing.
Amanda (wondering if she can assemble a second IKEA item in one night)