I'm American born, from Mexican parents, lived in the US all my life, have always spoken Spanish at home. I've found that I go by different terms depending on context and who I'm talking to

• I guess the most accurate term would be Mexican American
• Amongst my white American-born friends, usually I'll be Mexican (I live in Texas near the border, so Mexican is implied for Hispanics/Latinos)
• On government/federal forms, I'll be Hispanic (which they are careful not to label as a race). I'm mestizo (mixed), I have some european blood mixed with indigenous/native mexican. As a brown person, "White" doesn't quite fit, neither does "Native American". I alternate between "White" or "Other" pretty much randomly
• Amongst my Mexican-born friends, I'm the American, or pocho or chicano or gringo. But if there are other nationalities around like Peruvians or Spaniards, I'm culturally Mexican. Eg. tacos and churros are the food of my people.
• When I travel overseas, I go by American or Texan, and often get weird looks since I don't look like the Americans they see in TV and movies

While we are at it:

The one term I hate the most is "Latin music", when its used as a genre in a music store or a music app or used in a club. WTF is that even supposed to mean? They'll put music in spanish or portuguese, from different countries like Mexico, Brazil, Spain, Cuba, and even Puerto Rico and the US into a single category, which of course tells you absolutely NOTHING about the genre or type of music.

"Latin music" is useless as a label! Imagine if stores (or Spotify or itunes) had an "Anglo music" section, and put all of the Enlgish music from the US, England, Jamaica, Canada and India, and jumbled up Jazz, Country, Rock, Hip Hop, Metal, Folk, Raggae etc all into the same category. Madness!