Hi Anonymous,
...to a module's method when two modules have the same method name...
But if there's a conflict of method names, is there a way to unambiguously call a module's method?...

Though you have been given a great answer, I consider it not over "stressed" to say your requirements taste like an Object-Oriented in IMHO.
Since, the first two principle stated in perlobj answers thus:

1. An object is simply a data structure that knows to which class it belongs.
2. A class is simply a package. A class provides methods that expect to operate on objects.

So, awakening the Old dragon of OOP in Perl ( Yes, I know the "new" beasts ( Moose and it's different cousins ) are good extension of the Perl 5 object system ), one can do:

package Module1;

sub main {

    my $obj = shift;

    my $class = { name => __PACKAGE__, };

    return bless $class, $obj;
}

package Module2;

sub main {

    my $obj = shift;

    my $class = { name => __PACKAGE__, };

    return bless $class, $obj;
}

package main;

my $an1 = Module1->main();
print $an1->{name}, $/;

my $an2 = Module2->main();
print $an2->{name}, $/;

## And if you must use your dispatch table
## you can do

my %dispatch = (
    main         => Module1->main(),
    another_page => Module2->main(),
);

print "Am in ", $dispatch{main}{name}, $/;
print "Am in ", $dispatch{another_page}{name};
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NOTE:
All emphasis mine, to note my line of thought ( I hope, I didn't misinterpret the OP question)
both use warnings and strict were used though not stated.