I'll second the "don't do this". Given that you don't need to include the package name when referencing an exported symbol, what do you hope to achieve by having two separate source files, with two separate names, which contain alternate implementations of the same package?
Re: PERL modules named differently than the package won't export
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Version control of PMs where different callers (that is, different .pl files) can each choose which version of the PM they want by simply changing the use statement, not multiferous lines that call into the module.
Most functions are not exported; they have to be explicitly referenced (to avoid too much namespace pollution). But there are two or three that are used so often it just makes more clutter to require explicit reference.
This will (assuming I remembered the incantation correctly) make Utils1->import equivalent to Utils->import.
Although, really, the better approach would likely be to put the two versions of Utils.pm into different library directories (e.g., /usr/local/devel/Utils.pm and /usr/local/stable/Utils.pm), then manipulating @INC (by setting PERL5LIB in the shell or with use lib in the code) so that each program will load the appropriate version.