Core module overload allows you to overload dereferencing. If you overload hash dereferencing only, you may have it. Something like this, perhaps:

{
    package TwoFaceRefs;
    use overload '%{}' => \&getByKey;

    my %idx = qw(name 2); # And probably some more :-)

    sub getByKey {
        # Likely faster to return a tied hash,
        # but you get the idea ...
        my $obj = shift;
        return {map{ $_ => $obj->[$idx{$_}] } keys %idx};
    }

    sub dsfmm {
        # Assuming we get an arrayref:
        my $obj = do_stuff_from_my_module();
        bless $obj, "TwoFaceRefs";
        return $obj;
    }
}

my $obj = TwoFaceRefs::dsfmm();
my $name = $obj->[2];
#
# or
#
my $name = $obj->{name};
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Update: Comment and (a little) whitespace added.

Update 2: Oh, unless we make getByKey return a (properly) tied hash, assigning to the fields won't work:
$obj->{name} = "Sidhekin";
The original problem merely stated to access the fields, not setting them, but I just wanted to make it clear that this is one problem overloading (on its own) will not solve. (There is no problem overloading and tying together cannot solve. Well, okay. A few.)

The Sidhekin