Is it possible to be of a certain ethnic/origin but not identify as that?

For example, I am of Caucasian, Native and Hispanic descent. Because of my common Hispanic last name, many assume that's how I identify. I don't. I didn't grow up in that culture. I grew up with my grandparents who are of European descent. Yet, people get offended that I am not "Latina" and keep telling me to embrace who I am, not be embarrassed or scared, etc.
Is it possible to be of a certain ethnic/origin but not identify as that?
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