No they are normally named after the street they are on or close to. This is pretty much because pretty much every neighborhood has no sort of notoriety and name recognition except for a select few (i.e. Driftwood, Malvern, etc. which most people know). It's much easier to go by street name since that is what everyone in an area and across the city immediately recognize. For example every one has heard of Dufferin Street, but I can guarantee almost nobody has heard of "Fairbank" which just so happens to be the name of the Crosstown station at Dufferin and Eglinton. Obviously there are exceptions, some stations are named after people, places, and neighborhoods.
I personally don't really mind the names except some like renaming Eglinton West to Cedarvale which to me is a stupid thing to do, since EW has been around since the 70's and everyone knows it. Also Metrolinx said they wouldn't rename existing TTC stations and here we are. Other stations like Sloane and "Hakimi-Lebobic" are also silly but that's because imo they chose the wrong names (Sloane should be Bermondsey, and Hakimi-Lebovic, should just be Lebovic since these name have far more recognition in the area).