When foreigners came to the U.S. they often modified the spelling of their last name or even translated the name. Thus Schneider became Taylor. This happened even more frequently with given names because most names in European languages have an English equivalent.
A German named Franz, a Pole called Franciszek, and an Italian named Francesco could all easily become “Frank.” John is such a widely used name that it has many forms: Jan (Belgian, Czech, Danish, Gaelic, Polish), Hanna (Arabic), Ivan (Bulgarian, Russian), Hans (Danish, German), Hannes (Finnish), Jean (French), Johannes (German), Ioannes (Greek), Yohanan (Hebrew), Sean (Irish), Giovanni (Italian), Joao (Portuguese), Ian (Scotch), Juan (Spanish), Jonam, Jens (Swedish), Yochanan (Yiddish).
On the other hand a Spaniard named Diego, a Scotsman named Hamish or an Irishman called Seamus probably wouldn’t change to James. What you have to do is keep an eye out for is switching between the two names — in the Polish paper he may be Wojciech but in the city directory would be listed under Albert.
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