There is a broad literature that people with recognizably African-American names suffer from greater discrimination in the United States. (See here, here, here, here, and here.) Similar results have been found for Muslim names in France (here and here) and Sweden. In short, if you want your children to get ahead, even if you are a from a visible minority, give them a nondescript majority monicker.
There is some contrary evidence. Fryer and Levitt have argued that causality runs the other way, with black people trapped in the ghetto being more likely to choose distinctively black names than their middle-class counterparts. Their data, however, is only from California and is (as they admit) not conclusive. In addition, distinctive first names have become much more common in recent decades among all Americans, despite some evidence that people with such names face discrimination regardless of their race or religion.
So far, so complicated. But wait, it gets worse! Before 1960, having a distinctively black name may have helped. All other things equal, in the century before 1960 black men and women with black names lived a year longer than their compatriots, conditional on having made it to age 10.
In an amazing paper, Lisa Cook, Trevon Logan, and John Parman dug into the census data. First, they extracted a list of distinctively African-American names. Then they went through three million death certificates from Alabama, Illinois, Missouri and North Carolina between 1802 to 1970. Then they calculated differential death rates. Finally, they tried to see if having a distinctively black name was correlated with higher socio-economic status in any way. Overall, the reverse: as today, distinctive names were associated with lower status. In other words, the effect was even stronger than the headline numbers when you took other variables into account.
To be fair, it is still possible that there was name changing going on. But first, there is no evidence of such name-changing. And if there was, it would have to be mighty weird to change their results.
Their hypothesis is that having a distinctive name may have been a proxy for other, unidentifiable social capital: a strong sense of community, for example. And this was an age of open racial discrimination, during which assimilating to the dominant culture may have generated returns of zero (or negative, if white people reacted badly). So it may not have relevance for today.
But it sheds a fascinating look at the recent American past. Go, read.