One idea is that most of the recent immigrants such as Latin American mestizos and Asians could not pass for white and therefore see no point in trying to fool others by changing their surnames, in contrast to earlier waves of European immigrants who could blend in by looks. The article itself proves this idea wrong, so you wonder why they don't mention that. The current decline in Anglicization of surnames affects even European immigrants (one of the people featured is from the former Yugoslavia).
Plus before the decline, white-looking and non-white-looking both tried to adopt Anglo surnames. Ashkenazi Jews are a clear example of the former, and blacks of the latter. Blacks may not have been immigrants, but if there had really been a desire to emphasize their cultural difference, they would've changed their last names like Malcolm X or those who adopted Arabic surnames when they got into the Nation of Islam. Those few who did were lampooned by the majority of blacks for taking their African roots too seriously -- we're Americans first, they were saying.
And blacks could certainly not pass for white or Anglo, but only a clueless journalist or social scientist would think that's what influences the decision to adopt a certain group's surnames. Rather, it's about signaling the good faith effort they're making to leave behind the tribe they came from and join the one they've come to. It has nothing to do with signaling race.
They didn't even change them to something European but less Anglo -- they kept Jones, Jenkins, and Smith. Their first names started to diverge from whites' during the second half of the 1960s, but surnames are more important for identifying what Big Group you come from. Most people inappropriately project the '90s-era identity politics back onto The Sixties, which was about civil rights and anti-war. Black power was a fringe movement and vanished in a flash. Blacks wanted to join mainstream society so much that when three of the top ten TV shows featured all-black casts, they didn't try to blackify their surnames (or first names) at all -- they were the Evanses, the Jeffersons, and Sanford and Son. Ditto when The Cosby Show took over.
As late as 1984, we were still a very nation-oriented country, as the Los Angeles Olympics exemplified:
But the Los Angeles Games, televised by ABC, were a flag-waving, chanting USA ad...
"As a spectator at the Opening Ceremonies in 1984," NBC 2002 Opening Ceremonies producer Don Misher said recently, "I came out of the stadium euphoric. An IOC member later told me it was very nationalistic, second only to Hitler's (1936) Games."
You didn't see that at all in the Atlanta or Salt Lake City Olympics. Since the early '90s, it has become cool to be "ethnic," that is to de-nationalize the level that you base your identity on. Most of Robert Putnam's "Bowling Alone" narrative really applies to the '90s and 2000s, not the '60s through the '80s. If during the latter period people stopped playing bridge together, having friends over for dinner, and joining the PTA, it's because bridge ended as a fad as people took up other social games and sports (like softball), because people began to eat meals together outside the home, and because parents decided to get a life rather than hover over their kids and hound their teachers.
It was an incredibly social time, not to mention nationalistic. The public accepted or even cheered on a continual series of large wars and interventions, whereas during the '90s and 2000s politicians found out that they couldn't do that anymore, so we've had no large wars, let alone a string of them. If you weren't chanting "U-S-A!" during the Olympics, you got punched in the nuts for being a traitor. Since then it's become gauche and everyone will ostracize you for "jingoism." Right through the '80s, the description "All-American" was a complement rather than a put-down. That glowing image of the All-American showed up in popular music, too, from "California Girls" in 1965 to "Free Fallin'" in 1989.