By the way, one might logically guess that "crawfish" (речной рак) comes from crawl (ползать) + fish (рыба), thus signifying ползающая рыба ("crawling fish").

But in fact, the word "crawfish" comes from "crayfish", which comes from Middle English crevize, which was an уменьшительная форма (diminutive) of "crab" (крэб краб). And the word "crab" itself is cognate with Greek graphein ("to write"), and comes from an Indo-European root that means царапать ("to scratch").

So crab etymologically means тот, кто царапает and crayfish originally signified something like "crabette" -- meaning a маленький крэб краб.

From the original "crayfish" (произносится крЭйфиш) came the dialect variant "crawfish" (крАвфиш). "Crawdad" and "crawdaddy" probably came later, by folk etymology, based on "crawl". So "crawdaddy" = "crawl daddy" = ползающий папенька.

P.S. Thanks for the corrections, CoffeeCup!