• Why do you read into @data and the assign to new fields for every line??
• Why do you use slices in reading @data (@data[1] better written as $data[1], which would have been prompted to you when you would have used strict and warnings)
• Why do you quote scalars? (no need to put "'s around $Symbols)

Read ahead and see if that makes some sense:

use 5.16.2;
use warnings;

my $annotationfile = "file.tsv";
open my $fh, "<", $annotationfile or die "$annotationfile: $!\n";

# First read the header
my @hdr = split m/\t/ => scalar <$fh>;

my %GOHash;

# Now read every line
while (<$fh>) {
    chomp;

    # read as a hash
    my %hash;
    @hash{@hdr} = split m/\t/ => $_, 11;

    $GOHash{$hash{Symbol}}{$hash{"Taxon Name"}} = $hash{ID};
    }
[download]

FWIW you can read the whole file in one single statement into an array of hashes using recent Text::CSV_XS:

use 5.16.2;
use warnings;

use Text::CSV_XS qw( csv );

my $AoH = csv (in => "file.tsv", sep_char => "\t", headers => "auto");

foreach my $row (@$AoH) {
    print $row->{"GO ID"}, $row->{ID};
    }
[download]

scalar

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