Another reason outsiders and former members may dispute the name "Christian" for JWs, beyond just doctrine, has more to do with the everyday sense of the word "Christian" as meaning a good or a kind person.
In situations like where JWs allow a family member to die without blood. Outsiders might remark that it doesn't sound very "Christian" to them. Same with shunning, outsiders who hear about cutting off children might say, "and they call themselves Christian?"
But then I suspect we get closer to the heart of what the OP may be about, as certain vehement atheists might resent the equation of Christian with kindness or goodness, and therefore regard it as simply a label for a collection of superstitions they regard as equally applicable to JWs as to other groups. Which is okay as a perspective but we should be honest about the motivation and intention of the gesture. It's not intended as an inclusive gesture toward JWs but rather an attempt to bundle all professed "Christians" together and to disregard their own distinctions about what constitutes a Christian.