Martinez is not a Jewish name per se, It has no Hebrew root. The Jews from Spain Holds SPANISH last names, the Jews from Germany hold German last names, the JEWS from England holds English last names, the Jews from Russia holds Russian Last names.
And there are those last names which mixed the Hebrew root (the original) to a common part of naming customs in the zone they live and hide, like Levi, maybe the most common Jewish last name in Hebrew also Cohen, but Levi, a Jew from Poland mixed that to created "Levinsky or Lewinsky" etc. as well as termination "man" in English and German, ki or KY in slavic regions, ez or es in Spaniard regions etc.
A Martinez's birth name is Adolph Larrue Martinez.
Casper Martinez's birth name is Edil Martinez.
Ela Martinez's birth name is Mariela Martinez.
Ferny Martinez's birth name is Fernando Martinez.
Anastacio Martinez's birth name is Anastacio Euclides Martinez.
Angie Martinez's birth name is Angela M. Martinez.
Buck Martinez's birth name is John Albert Martinez.
Carmelo Martinez's birth name is Carmelo Martinez Salgado.
Doug Martinez's birth name is Douglas Vincent Martinez.
Rayven Martinez's birth name is Rayven S. Martinez.
Shelly Martinez's birth name is Shelly Lenore Martinez.
Sophia Martinez's birth name is Sophia M Martinez.