Named after a relative who married a Gentile

I was named after my grandmother’s cousin. I learned recently that my namesake had married a Gentile. Should I consider adding to this name or changing my Hebrew name?

I don't think so, for almost every name you can find a Tazdik and the opposite. If the name is a common Hebrew name you can consider it to be after a righteous man with the same name, how much more so if you are not called often by your Hebrew name. All in all, names are not something we play around with. If you wish you can consult with some great Kabbalists and Torah scholars like Rav Mordechai Eliyahu whom have a better grip on names and their Kabbalistic impact than me.