You're looking for symbolic references (aka "getting a variable name from a variable"). It's rarely a good idea to use symbolic references in a Perl program - which is why they are one of the features that "use strict" disables.

It looks like what you want here is an array of hashes.

my @data;
for ($i=1; $i<=$number; $i++) {
  open (LOOKUP, '<', "file$i");       
  while (<LOOKUP>) {
    chomp;
    my ($ref_name, $ref_id) = (split /\t/, $_)[3,4];
    $data[$i]{$ref_id} = $ref_name; 
  }
}
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See perldsc for more details on building Perl data structures.