I can't speak to the "prevalence of Qs". But at least I can at least address part of your question, which is the prevalence of names adapted from Arabic. At least here, your dad was on to something.

During this period (1960s), in large part through groups like the Nation of Islam and Nation of Gods and Earths, there was a rise in association of Black identity with the perceived religious roots at the time that one's ancestors may have been brought over. By the 1500s and through the height of the trans-Atlantic slave trade, Islam had spread through North Africa and most of West Africa. While a good number of slaves headed to North America weren't necessarily coming from the Islamic world (which it not to say none of them did), the perception was still there. It wasn't really a return to Islamic roots, though, as much of what the Five Percenters follow/ed would be outright heretical to mainstream Islam, and the Nation of Islam wasn't much better (hence Malcolm X's eventual break from NOI). Still, it became popular to take Arabic names as a clear break that still had some perceived ties to history. Many of these names are still somewhat common, such as Jaleel, Aisha, Jamal etc.

For more recent developments, I'd only be speculating, so I'll leave that to someone else.