The majority of my blood ancestors hail from Fujian province in China, where our last name was originally pronounced “Tsai”. They were merchants and traders (with the occasional scholar somewhere back in the family line). At some point, largely between 2-4 generations ago, they immigrated to the Philippines, where they were doing most of their business. My grandparents more or less grew up Chinese, and we consider Chinese-ness to be the root of our cultural heritage.
Most of my still-living extended family grew up in the Philippines (Aparri and Manila) as part of the Chinese-Filipino community. Their name was spelled “Chua,” pronounced “Tchwa,” a romanization of the Chinese name “Tsai.” This included my parents, who more or less grew up Filipino (or Chinese-Filipino, really). They still consider the Philippines to be home, and I consider the Philippines to be “where we're from.”
My parents then proceeded to immigrate to the United States, where my brother and I were born and raised. We speak English as our (only) native tongue, attended US public schools, and otherwise grew up American. We just happened to visit the Philippines a lot, eat a good deal of Chinese and Filipino food, call our family members by Fookien (the Chinese dialect spoken in Fujian province) names.
The end result of this long story is that I basically tell people that I'm Chinese-Filipino-American, but the shortest way to explain it is really “American.”