The modern English word can be traced back to Proto-Germanic *sturkaz. Nearly every Germanic language has a descendant of this proto-language word to indicate the (White) stork. Related names also occur in some Eastern European, languages, originating as Germanic loanwords.
According to the New Shorter Oxford English Dictionary, the Germanic root is probably related to the modern English "stark", in reference to the stiff or rigid posture of a European species, the White Stork. A non-Germanic word linked to it may be Greek torgos ("vulture"). (en.wikipedia.org/wiki/Stork)
The polish name of this bird - "bocian" originates from the Mayan bo-ciahn which stands for "he who brings the children".