This trend started some time in the late '80s with people making up pseudo-African names - and since then it has spun out of control.
Honestly though - I don't think I could care less. If one likes their given name, good. If one doesn't, then one can have it changed. No big deal.
I think your time estimate is about right, maybe 5 or 10 years earlier.
"Unusual" names don't bother me either. I've worked with lots of people from east and south Asia. Some take "English" names, some don't. With the ones who don't, I try to learn how to say their name, and they have patience with people who do so imperfectly (try pronouncing "Thiagarajan") and/or suggest shortened nicknames (e.g. "Raj").
Two things do bother me about giving kids faux-frican names.
First is the separatist attitude that demonstrates. Trying to maintain fortress-like separatism in a larger society turns out badly, for all concerned.
Second, in the real world, especially among children, giving bullies easy pretexts for bullying is poor parenting, at best. I realize bullies will bully, but why make your children easy targets?