So the end result for HIPPO1 and HIPPO2 should be the same, right? Assuming that, the following ends up with HIPPO as a key (no number -- just the 'root' name) (note that hashing on the 'root' animal name also eliminates the need for the nested looping over bigHash):

my %animals;
while( my ($state, $zoos) = each %bighash ){
  while( my ($zoo, $row) = each %$zoos ){
    my $animal = $row->[1];
    $animal =~ s/\d+$//;
    push @{$animals{$animal}->{$state}}, $zoo;
  }
}
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Note in your original code that @zoos probably shouldn't be globally scoped.