Yes, whatever name would have been spelled in Cyrillic
letters for Russian, and Hebrew letters for Yiddish.
Just like Peking became Beizing and Bombay became
Mumbai with different transliteration methods, our
ancestors surnames often became somewhat changed.
Generally, the intention was usually to keep the sound
the same, but, for example, Yiddish was pronounced
differently in different areas. And spelling was not
consistent until well into the 20th century in
English. Also, things got mangled and simplified.
However, Sawalkin probably came >from Suwalki, a big
city and gubernia in Russian Poland. The sound is