The last name "Sarkar" has Persian roots...does that mean all Sarkars have Persian roots?

-i know for a fact, that the last name "Sarkar" is common for bengali people...but the name itself has origins in Persia...i also know some bengalis have ancestry roots in persia...so is there a correlation between having a last name rooted in Persia, and having actual ancestry roots in persia??Sarkar is the word to call a "Sargent" And means "On Duty" in Persian!