It is indeed a stretch, but it's just supposed to be an evocative name not a perfect analogy. In particular, quantum Darwinism has a notion of fittest types of information, and this information is replicated, but it crucially does not feature a notion of mutation, so in particular it cannot result in increasing complexity/sophistication over time as produced by biological Darwinism.
Evocative "sorta" names have a tendency to spread misinformation when the scientific details are opaque to most people. It's not a practice that I think is okay.
Then you should probably express your displeasure to guy who picked the name :)
Seriously though, all evocative names are imperfect. Laymen always over interpret them. I don't like "quantum Darwinism" much, but if your standard is that the name of a
mathematical concept not be misinterpreted, then basically all English words are out.
