Is Stein a Jewish name?
No, It's a German name meaning stone. You can be Jewish with a German last name. Note that some people who move to a new country don't keep their old surnames and they pick knew ones or their named after their occupation. My mothers family on one side were trappers so they were named Fanger (meaning trapper or to catch). I also know of some Jewish family's with the last name Roth and my last name is Roth but my family is not Jewish Roth ( meaning red in German ). People were named Roth usually because of their red hair. So basically not everybody with Stein as a last name is Jewish.
It's possible for someone with the last name of Jenkins to be Jewish, but it's certainly not a stereotypical Jewish name. "Jewish" names in the US tend to be Germanic or eastern European, because of the large number of Jewish refugees from those areas that emigrated to the US in the mid-20th century... endings like -baum or -berg or -stein or -mann or -ski/sky are fairly common, for example.
Stein means 'stone" in German, many Jews are of German extraction like many Scandinavian names end in 'son" eg: anderson, Peterson, Emmerson, etc. -stein isn't a Jewish name, it's a German name (the same is true of -berg and -mann). By the time last names became common ("Thomas Miller" as opposed to "Thomas the Miller"), there were many Jews living in Europe. They took names in the language spoken in the region they lived in…