Correlation is not causation. It's entirely possible that children with those names actually do tend to be naughty. You can't possibly say in which direction the causation is working should there be one.
No, which is why I said ‘may’ rather than an absolute.
However you do need to look at what’s likely, based on the other evidence we know about unconscious bias, confirmation bias and other aspects of human psychology.
Is it likely that a certain combination of letters leads to a naughty child, or a bright one? We can probably cross that one off the list.
Is it likely that perceptions behaviour and intellect are associated (rightly or wrongly) to class and ethnicity, and therefore names associated with certain subsets of social class and with certain ethnicities are assumed to take on those characteristics.
Is it likely that at least some teachers, who are fallible humans with the same tendency to bias as the rest of us will, having decided that Elizabeths are bright and Chelseas are naughty, that Williams go to university and Callums go to detention, will unconsciously treat children with those names differently?
It would be amazing should teachers behave entirely differently from recruiters for jobs, where a clear and active bias has been repeatedly found based solely on names.
Making assumptions is not always unfair and mean/nasty/etc. Because the thing is, when someone looks at a name of the type being talked about here, and thinks "bet they didn't go to Oxford/are highly educated/come from money/whatever", the chances very much are they are correct. And actually, therein lies the real problem that we should care about.
I’m struggling to see a positive element of someone making an assumption (rather than seeking objective evidence) about an individual based on their name in the contexts discussed on this thread, whether it’s about their education, their skills, their intellect, their ambition, or their suitability to do a certain job.
Because it is a problem when someone thinks ‘bet they didn’t go to Oxford’ based on a person’s name. It’s part of a wider problem but is in itself a barrier to social mobility.