What's your question? What are you having difficulty with? What have you tried?

It rather looks like you think you can post a specification here and someone will do your work for you.

You are going to be on a very steep learning curve with Perl. But to get you started, I would create a hash table out of file2. This will allow you to translate any TID into the SPNAME. Code below. Note how I limited the number of things coming out of the split(). You will need that technique to parse the first file, except there will be 3 fields instead of 2.
 my ($gid,$tid,$concat) = split(/\s+/,$_,3);

#!/usr/bin/perl -w
use strict;
use Data::Dumper;

my %tid2spname;

foreach (<DATA>)
{
   chomp;
   my ($tid, $txt) = split(/\s+/,$_,2);
   $tid2spname{$tid} = $txt;
}

print Dumper \%tid2spname;

__DATA__
10090   Mus musculus
10116   Rattus norvegicus
148305  Magnaporthe grisea
28985   Kluyveromyces lactis
33169   Eremothecium gossypii
3702    Arabidopsis thaliana
4530    Oryza sativa
4896    Schizosaccharomyces pombe
4932    Saccharomyces cerevisiae
5141    Neurospora crassa
5833    Plasmodium falciparum
6239    Caenorhabditis elegans
7165    Anopheles gambiae
7227    Drosophila melanogaster
7955    Danio rerio
9031    Gallus gallus
9598    Pan troglodytes
9606    Homo sapiens
9615    Canis lupusfamiliaris
9913    Bos taurus
[download]

I have given you the code, that i wrote....

use strict;
use warnings;

open (HOMOLOGENE,"<homosample.txt") or die $! ; 
open (TAXID,"<taxid.txt") or die $! ; 
open (HOMOOUT,">>homooutput.txt") or die $! ; 

my @gid;
my @homotaxid;
my @taxtaxid;
my @species;
my @gene;
my $newgid;
my $newgene;
my $homolen;


# While loop for reading the data from the Homologene.

while ( my @homo=<HOMOLOGENE>)     # @homo - > @inputs      
{
    $homolen = $#homo;   #homolen -> arraylen
        
    for (my $i=0;$i<=$homolen;$i++)
    {
        chomp $homo[$i];
        my ($one,$two,$three, $four,$five,$six) = split(/\s/,$homo[$i]
+);
        chomp $one;
        chomp $two;
        chomp $four;
        chomp $six;
        my $concat1=join(' | ',$four,$six);
        chomp $concat1;
        push @gid,$one;
        push @homotaxid,$two;
        push @gene,$concat1;
    }
}
# print @gene;

while ( my @tax=<TAXID>)       
{
    my $taxlen = $#tax;   # taxlen for tax array length
        
    for (my $j=0;$j<=$taxlen;$j++)
    {
        chomp $tax[$j];
        my ($seven,$eight,$nine) = split(/\s/,$tax[$j]);
        chomp $seven;
        chomp $eight;
        chomp $nine;
        push @taxtaxid,$seven;
        #$, = '::::';  # separation character
        my $concat2=join(' ',$eight,$nine);
        push @species,$concat2;
        #$, = '::::';  # separation character
    }
}
# print @species;
my $specieslen=$#species;   # Species length

for(my $l=0;$l<=$specieslen;$l++)
{
    print HOMOOUT "\t\t\t\t\t".$species[$l]."\t\t\t\t\t";
}

print HOMOOUT "\n";

close HOMOLOGENE;
close TAXID;
close HOMOOUT;
[download]

Yes, you have given us the code and a specification. What we would like to know is exactly what is the problem you are having with the code you have posted? What is it doing that you think is wrong? We do not know your problem unless you state it.

I could run your code and see what problems I encounter, but I should not HAVE to do that. You should provide an explanation of your problem. If you do provide a good explanation of the problem you are having you will probably get several good responses.