my %vars = (
            MyArray => \@MyArray,
            HisArray => \@HisArray,
            OtherArray => \@TheirArray,
           );

my $ref;
unless( exists $vars{ $MyScalar } )  {
  die "Error: Don't know about '$MyScalar'\n";
} else {
  $ref = $vars{ $MyScalar };
}

## Use $ref . . .