It was not only the "I/Y" that was removed from the start of names. Yiddish-speaking Eastern European Jews, especially in Poland (the country with which I'm most familiar), tended to swallow the first letters of words and names when speaking, for example saying "chbin" for "ich bin" (I am) and "dvelst" for "du velst" (you will). Names were often abbreviated by dropping the first syllable/part of the name, especially if it was unstressed (as opposed to what happens in the English-speaking world, where it is more common to drop the END of the name). Thus Alexander (which would be abbreviated to Alex in an English-speaking country) becomes Sender in Poland, Emanuel becomes Manel, Efraim becomes Froim, Yeshaya becomes Shaya, Israel becomes Srul, and so on. I can easily see a Polish Jew turning Italienner into Talyener/a. 

All the best,