I have two main things to say.
Contrary to 90% of the population, I can see where she is coming from. As a teacher, I know or have known thousands of kids. Most people probably know up to a hundred. There are names that I, as a teacher, am wary of. If I see a list of names, there may be some that make me think 'I need to watch that kid'. My wariness may turn out to be completely misplaced, but there are some names that tend to be more troublesome than others. Of course, all kids are individuals, but it is nevertheless a fact that there are certain names that are more likely to be trouble than other names.
In fact, surnames can be even more significant. Sometimes surnames can indicate a child's likely background and therefore what they might be like.
This is not to say that I would treat kids with such names any differently in practice (I wouldn't stop my child from being friends with someone just because of their name) but, as far as I can tell, from a relatively large sample of teenagers, there are some names that tend to cause more trouble than others. There are, of course, exceptions - this is a generalisation at best. I disagree with Katie Hopkins' decision to stop her children being friends with kids with certain names, but her decision is, at least, based on generalisations that are true.
My second point is that we all judge kids (and adults) in ways that we shouldn't. By their names, their clothes, their accent, vocabulary, address, friends, car, house etc. The people who are so angry with Katie Hopkins for making assumptions about people based on their names should have a look at the assumptions they themselves make about people based on these things.
There you go. Shoot me down if you want.