I've considered changing my name since the first day I understood that names could be relatively normal. You see my kind parents thought it would be endearing to name me Dusty. Suffice to say, I've had a hard time projecting a certain sort of image for myself with a name like that. The only merit I've ever noted in my birthname is recognition. For better or worse, no one forgets a Dusty. I try to diffuse some of the negative image by shoehorning in humor, "hello I'm Dusty, like the adjective," but eventually I'm going to have to get it changed...
Nobody's infallible. What kind of rationalist approaches a work with a couple holes in it and leaves under the assumption that the writer is simply so perfect that everything will be addressed and wrapped up neatly by the end? Isn't it far more likely that in writing a fantastic teaching tool/test, Eliezer occasionally leaves a thread or two hanging?
Actually the ministry has a trace spell, evidently, on the whole of magical Britain. Magical misdemeanors from underage wizards go largely unpoliced in all magical households, explaining the fact that several familys, such as the Malfoys and the Weasleys have sent children to Hogwarts who openly acknowledge having learnt spells outside of Hogwarts. You may recall, once the ministry was in Voldemort's pocket, the trace was used to track down underaged wizards not in Hogwarts. I'd always supposed Hogwarts worked in conjunction, or possibly with special permissions, from the ministry to use the trace to send letters to children who had performed slight magical acts, such as Harry phasing his cousin through the glass at the snake exhibit.
I'm not sure about that, if anything she's put on Pottermore is to be trusted, she's written an extensive off-page history for her world. The most interesting example is what she's written about the Malfoy's. Evidently, the family made most of their money in dealing with muggles prior to the ministry instituting the laws regarding secrecy. Once it became politically favorable to distance a prominent family from muggle ties, the Malfoy's put on a strong pureblood facade that caught on after a few generations.
I could be wrong here, but I definitely remember someone, maybe Hagrid, claiming early on that Hogwarts was, "the best school in magical Britain." That implies others. It's entirely possible that newer magical schools without a history of legendary wizards and a past alliance with two other prestigious schools would go largely unmentioned in the original Harry Potter.
I am always amazed that everyone doesn't assign a pocket to things. It's something I'd honed as far back as middleschool after repeatedly loosing my camera due to a messenger bag without a zipper and a tendency to set things down less than carefully.