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.
Katherine Jenkins' Mum's name is Susan Jenkins and her Father's name is Selwyn Jenkins.
Mel Jenkins's birth name is Melvin Jenkins.
Ab Jenkins's birth name is David Abbott Jenkins.
Alfred Jenkins's birth name is Alfred Donell Jenkins.
Amber Jenkins's birth name is Amber Renee Jenkins.
Carter Jenkins's birth name is Carter Mark Jenkins.
Chelsea Jenkins's birth name is Chelsea M Jenkins.
Cullen Jenkins's birth name is Cullen Darome Jenkins.
Ferguson Jenkins's birth name is Ferguson Arthur Jenkins.
Herbert Jenkins's birth name is Herbert George Jenkins.
Megs Jenkins's birth name is Jenkins, Muguette Mary.
Patty Jenkins's birth name is Patricia Lea Jenkins.