The 2016 election is fascinating and unprecedented for several reasons. One reason is that there are two Latinos running for the GOP nomination, and are considered to be favorites of the party establishment. Marco Rubio and Ted Cruz are both freshmen senators, both are of Cuban ancestry, and both are sons of immigrants (though they don’t favor an easy pathway to citizenship for newcomers).

But that’s where the similarities end as far as how they wear their cultural heritage. This New York Times piece says that in their approach to their Hispanic identities — traits that can make or break their success in courting both Latino and non-Latino voters — the two sharply diverge, starting with their names and how Ted Cruze chose to anglicize his name.

His preference for Ted, a suggestion from Mr. Cruz’s Irish-American mother, infuriated his father, Rafael, who in 1957 fled Cuba for Texas after being arrested and beaten by agents for Fulgencio Batista, the Cuban dictator. “He viewed it as a rejection of him and his heritage, which was not my intention,” Mr. Cruz wrote. For two years, his father refused to call him Ted. Today, Mr. Cruz serves as his son’s Spanish-speaking surrogate.

The name change is but one example of how Mr. Cruz has de-emphasized his Latino identity. Unlike Mr. Rubio, Mr. Cruz had only his father and a few relatives to connect him to the island, its language and traditions. Once his father became a born-again Christian, religion, not ethnicity, appeared to dominate the Cruz household.

“His approach to all the people with whom we interacted was who they were, not what they were,” said David K. Panton, Mr. Cruz’s former roommate at Princeton University and Harvard Law School.

On the stump, Mr. Cruz has embraced his Cuban father’s story, more for what it says about America than what it says about immigrants. His father fled Cuba with $100 sewn into his underwear and worked as a dishwasher to help pay tuition at the University of Texas at Austin. “America, quite simply, saved my father,” Mr. Cruz wrote.

The story is a poignant one, but many Latinos have said it falls flat for one reason: The pride Mr. Cruz feels for his father is not one he extends to the larger immigrant community.

We would say to the GOP if they’re listening that they need to have a stronger understanding of the Latino communities in the U.S. There is a lot of talk in political circles about how Cruz or Rubio would attract Latinos just based on their roots. But the Latino community is hardly monolithic and, even more to the point, many Mexican-Americans could give a damn that a Cuban-American running for President.

If just having a Latino name on the ticket is the party’s idea of Latino outreach, they are going to be severely disappointed.