Inconsistent names were found using the following regular expressions.
* `rg "TEST(_F|_P)?\(\w+,\s+\w+Test\)"`
* `rg "TEST(_F|_P)?\(\w+,\s+Test\w+\)"`
* `rg "TEST(_F|_P)?\(\w+Tests,\s+\w+\)"`
Fixes#3495.
The old headers were moved into folders because doing so avoids polluting
the system include directories.
Folder names were also normalized to lowercase.