Is it wrong for me to keep my last name even after getting married?
It is common in Western culture for the woman to take the last name of the husband. Essentially it goes back to a concept that she is now his property. In America it is no longer required, and among some not even expected, that a wife assumes her husband's last name. In the business world it is even common for some women to keep their former name for business but use the husband's last name socially.
Is it wrong? That depends on the social situation, perhaps. Is it sinful? Since the Bible doesn't address the question at all, I don't think anyone could prove it was a sin. Since last names were generally not part of the culture when the Bible was written it is silent on the matter. There is mention of surnames, but no indication that they were passed on to the children or that the wife took that surname.