What you are thinking of is some kind of a closure, like this:

my $make_output = sub {
    my ($Registration, $Rank) = @_;
    return @{ $Data{$Registration}->{Name} }[$Rank], "\t";
};

print $make_output->($Registration1, $Rank1),
      $make_output->($Registration2, $Rank2);
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Though I guess that you might be able to simplify your code by using techniques such as OO.

Update: The following code shows what an OO variant would look like. Maybe you are trying to do something completely different; but according to your short line of code, I imagine that you could probably use this example.

my $data = Data->new( ... );
print $data->make_output($Registration1, $Rank1),
      $data->make_output($Registration2, $Rank2);


# class definition
package Data;

sub new {
    # set up data object
    # ...
}

sub make_output {
    my ($self, $Registration, $Rank) = @_;

    return @{ $self->{$Registration}->{Name} }[$Rank], "\t";
}
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