Halpark is correct. The manifests were created at the ports of departure by agents from steamship companies not by English scribes. The info was taken from passports or travel papers obtained in the immigrants homeland. One such agent was Laguardia (who would later become mayor of NYC). He worked at the port of Rijeka (aka Fiume) and spoke Italian, Croatian and Hebrew.
Someone coming from a country using the cyrlic alphabet would have had to have their name translitered into the Latin alphabet