Not really, I think the official name is "hűtőgép" or "hűtőszekrény" as in cooling machine and cooling cabinet, although there's the joke my grandpa like, when we complain the food is hot: "Nem jégszekrényben főtt", but obviously, the joke is probably as old as him :D
Interesting, my family calls it a jégszekrény as well. Because I learned Hungarian from my grandparents it's interesting to see how the language and accents have changed when I learn on here or visit Hungary.
Well, "fridzsider" should sound familiar. "Frigidaire" is an American brand name for a line of home appliances. The name comes from their early cooling appliance line of refrigerators and freezers.