Best way to think of this is as “near” and “far.” The ethnicity you were born into can well be far, while other ethnicities are near. For example, I’m Cajun, both of my parents are Cajun and their parents are all Cajun. But my mom moved out of South Louisiana when I was 9 or so after marrying a guy in the military.
Cajun is far to me, while Ethiopia, a culture that I have no birth connections with, is very near to me, because I’m dating a girl from there. Her adopted culture is America, because, just like me, the Ethiopian culture she was borne into is not where she spent the last 10 years.
It’s hard for me to think of myself as Cajun. My lady hardly thinks of herself as Ethiopian.
Despite all this, it’s important to not totally discount your heritage. So much of the ‘deep self’ comes from there. So many of my behaviors stem from things I picked up from my parents, who picked it up from their parents. Even if your ethnic heritage is far to you, it’s not far to your subconscious, so you should treat it as a part of your identity anyway.