They are actually Spanish names, not "Mexican" names, but I'm not sure why it would be a shock that these persons would have Spanish names. Hispanics are a very large portion of the "white" population of Texas, especially around San Antonio and the Hill Country. Many of these family lines have lived in Texas for hundreds of years, when Texas was part of Mexico.
Why do you think it is relevant that they have "Mexican" names?
I'm going to tell you a true story (it's short, not really relevant, but your post reminded me of an incident over several months ago).
My wife and I went downtown to eat at Laziza (Laziza Mediterranean Grill, there are two in the Augusta area). We had ordered and just received our food when there was a woman yelling at the staff.
Over the summer there was an effort to get people to support only Black owned businesses (yes, racism, but not the point). By this time the "Black only" push had ended (Augusta is 65% Black, White's make up about 35%, so the demographics were different from much of the nation.).
Anyway, the problem in the line at Laziza Mediterranean Grill is this women went there because she thought it was a Black owned restaurant and it turns out the place is owned by Nader Khatib, who is not Black. She accused them of racial appropriation by naming their restaurant "Laziza Mediterranean Grill" because Laziza sounds (to her) African-American. (Laziza is an Aarabic name).
Anyway, I just thought that was interesting. You are right that it is wrong to judge people, and it is wrong to judge people by their names.