Correction - all the folders used to have, and should have had the same permissions, so I didn't actually check. I don't know how the permissions came to be reset; I suspect when copying the files from desktop to laptop and back again. Why it should only affect those with underscores is also a mystery. Anyway, they all have the same permissions now, and things are mostly working.
I tried this, which was when I spotted the problem with the permissions. After I sorted that out, I tried again. I made two copies of MySite, called My-Site and My_Site. All three have identical permissions. I also made two copies of Another_Site, called Another-Site and AnotherSite, again with the same permissions as the first three.
With the corrected permissions, MySite works, as does My-Site, but My_Site throws a 404 error. On the other hand, Another_Site now works, as does Another-Site, but AnotherSite throws a 404 error. Weird. At least it looks as if all my sites will work with their original names, provided I double-check the permission.
I don't have VirtualHost set up for anything, as far as I'm aware. (Nor do I have conf/extras/httpd-vhosts.conf - not even those directories.) I'd got as far as installing PHP and simply copied a site to the web root to check it would work. It threw a 403 error, so I tried another and eventually discovered the underscore problem. I hadn't attempted to configure anything.
I'm not sure I follow that. There is no connection between MySite and Another_Site. They're two completely separate sites (or, more accurately, stand for two sets of independent sites, one with single word names and the other with underscores) which I was using independently to test.
Thanks, all, for the help.