You've named your packages one way, and your files another.

The package named in Module.pm could be called anything, and indeed, multiple packages (and more use Another::Module statements) may be present. If you want to do the Perl equivalent of putting your coat on front-to-back, be prepared for awkwardness (and the odd chuckle from the peanut gallery).

But we've all done silly, nay, even stupid, stuff before. Some of us even admit to it. Welcome to the club! I hear the members are of the highest quality!