Like I hinted in Re^3: Appending $VERSION to package name in Makefile.PL , do not install your module, don't overwrite existing installs, don't rename the module name

Renaming the module is the wrong solution (whether from Makefile.PL or otherwise). If you want to rename something, rename the directory where the module gets installed.

Telling Makefile.PL to install the module in a custom directory is one option.

Simply not installing the module at all (not running Makefile.PL) is another option.

Distributing a binary ( a complete perl ) is another option

I provided several links (and links to links), if you're interested how each solution works, you should follow them

You can also see an overview of the different variations of these solutions at the slideshow linked at Seen in PerlWeekly newsletter: Carton CPAN dependency manager