Also, various low level processes behave in a Darwinian fashion: most significantly, neurite tips are copied with selective retention, and nerve impulses themselves are copied as they travel down branching axons and up branching dendrites.
I think that it makes reasonable sense to refer to these low-level brain processes using the term 'Neural Darwinism'. There's a bit of a problem though - which is that the term 'neural Darwinism' has been widely used to refer to the particular theories put forth in the late Gerald Edelman's 1987 book titled neural Darwinism.
Gerald Edelman was a pioneer in applying Darwinism to the brain - and I don't want to diminish his contribution too much. Developmental selection is a reasonable idea. Experiential selection is a bit more of a dubiously-named idea. I read neural Darwinism in the 1990s and found it dry, tedious and unconvincing. However, retrospectively, Edelman's concept of neural reentry looks important. It could be the key to understanding how the brain does something functionally similar to back propagation without having a good quality bi-directional signal propagation mechanism.
Overall, though, I think things have moved on a bit since 1987. It is now clearer that there are at least three types of low-level signal copying in the brain: the conventional reproduction of cells - including neural stem cells, the splitting of axon and dentrite growth tips, and the splitting of signals travelling how axons and back-propagating up dendrites. Despite the progress, I think we can still use the term "Neural Darwinism". I would hate "Neural Darwinism" to become a reference to an out-dated and discredited theory: it deserves better than that.
Signals propagation in axons and dentrites has been effectively simulated by synthetic neural network enthusiasts. However few of them bother simulating the other main copying processes in the brain: cell splitting during development and neurite tip splitting. Maybe simulating these Darwinian brain processes would help to build better synthetic neural networks.
For references see my Keeping Darwin in mind essay.