Indeed the Torah says that Ashkenaz was a grandson Yefet. However Ashkenazi Jews are not from the Bible personality Ashkenaz. They as all Jews come from Abraham.
Ashkenaz is the Hebrew word for Germany whose original inhabitants may have been the descendants of Yefet. In the Middle Ages a good portion of World Jewry lived in Ashkenaz/Germany-France and Sefard the Hebrew word for Spain. Over the years different customs and cultures developed among these two groups. Despite the migration of the Jews from Spain after the inquisition, the Jews of Spanish descent retained the title Sfardim. The same with the Ashkenaz Jews who moved deeper east into the various European countries such as Poland, Russia, etc. yet continued to be known as Ashkenazim
I hope this helps.