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There are many different Adler families since Adler is a popular name in German speaking places.
One family has a story that the Emperor Franz Joseph of the Austro Hungarian Empire named three brothers for their service to him while he was in present day Romania. The three brothers were each given a surnames Adler, Fruchter, and Stern.
Another is that of the Family of Natan Adler of Frankfurt am Main, a Cohen, the Eagle with spread wings symbolizing the Cohen's fingers when making the Priestly Blessing.
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Balázs Déri says :
Some Adler families may descend from Adalla from Park clan king of Silla ( Singra ) between about 1233 and 1203 b.c. corresponding to 154 and 184 of Europeans counting years from 1387 b.c..
See Pak,German,Hermann,Schillinger,Musikant,Tarasco,Alamán,Andaluce and more !