My name is Shankaranarayanan. If you know me you can call me shankar. I don't have a last name. Most Indians do not have a last name. When western forms and westerners ask for our last name we make that stuff up.
I usually use my father's name Gopalakrishnan as a last name but it is not a true last name. Some will use their caste name but these are endogamous family groupings. We have a gotra name that is an exagamous family grouping name analogous to last names but it is used only at the time of marriage not for everyday use.