You seem to be ignoring the earlier statistical complaint by the other poster. They are implying a null hypothesis where names signal socioeconomic status and discrimination may be on that status rather than race.
To test for this, you cannot start with unequally characterized populations (black and white) and compare equally popular names from each population. You need to first stratify by socioeconomic status and then draw popular names from equivalent sub-populations. E.g. equally popular black and white names among babies born to households with lowest quintile income and high school as the parents' terminal degrees; equally popular black and white names among babies born to households of middle quintile income and 4-year college degrees; etc.
But more to the point, racial discrimination has been replicated by many studies constructed in different ways. A famous 1978 study found discrimination when sending equivalent resumes that had a headshot of either a white or black person attached. Other studies have looked at including extracurricular activities that imply a certain race.
Explicitly filtering by race is bad. However, if it leads to the same outcome as filtering by qualifications, then forcing people to switch hiring practices doesn’t actually improve anything.
The blame shouldn’t be on the hiring process, but instead (at least in the US) by the politicians that have set up our cities and schools to be systematically racist.
(I still think this is a bad SCOTUS ruling, to be clear.)
The names in the NBER study were drawn from actual birth certificate data correlated with race. It was not a subjective choice from researchers. Latonya was used because Latonya was the first name given to 4.7% of the black female babies born during the study period. Just like Allison was 4.7% of white female babies in the same data.
If you perceive common African American names as lower class than equally common white names, I believe that's part of what the study is trying to demonstrate and not a flaw of its design.