This is a common bioinformatics problem which we can generalise as "I want to read a fasta file and do something with it." Since you are using Perl, you should be using Bioperl and in particular, the SeqIO module.

You need to break the problem down into a series of steps. They are:

1. Open file containing file names and identifiers
2. Step through each line and extract file name
3. Open corresponding fasta file and append identifier to header

I'll assume that your fasta files and the file of file names are in the same directory. I'll also assume that your fasta file names are as given, i.e. they contain a space and have no suffix. This is not good practice and I'd suggest renaming the files to something like Nostoc_punctiforme.fa. You don't say whether the fasta files contain protein or nucleotide sequences but a good convention for suffixes is that used by the NCBI: .faa for protein, .ffn for nucleotide and .fna for nucleotide single sequence (e.g. a chromosome).

I'll also assume that (1) the columns of your text file are tab-separated, (2) the file is called ids.txt, (3) you want to write to a new file with the suffix .mod, containing fasta sequences with the modified header and (4) the identifier should be inserted directly after the ">" in the header.

#!/usr/bin/perl -w
use strict;
use Bio::SeqIO;

# open text file
my $file = "ids.txt";
open IN, $file;
while(<IN>) {
  # remove line endings and split on tab
  chomp;
  my @line = split("\t", $_);
  # check fasta file exists and open
  if(-e $line[0]) {
    my $fa = Bio::SeqIO->new(-file => $line[0], -format => "fasta");
    # create new fasta file for modified output
    my $outseq = Bio::SeqIO->new(-file => ">$line[0].mod", -format => "fasta");
    while(my $seq = $fa->next_seq) {
      my $id = $seq->display_id;
      # modify header
      $id = $line[1].$id;
      # modified sequence object
      my $newseq = Bio::Seq->new(-id => $id, -seq => $seq->seq);
      # write modified sequence to file
      $outseq->write_seq($newseq);
    }
  }
}
close IN;

Result using a small test file named Nostoc_punctiforme:

INPUT Nostoc_punctiforme
>seq1
agagagagagagaga  
>seq2
gatacatagatacag

OUTPUT Nostoc_punctiforme.mod
>NOPUseq1
agagagagagagaga
>NOPUseq2
gatacatagatacag

One the solution would be to:

1. read your sample file line by line
2. split each line int filename and postfix tag
3. now read the file line by line
4. if the line starts with the > symbol append the postfix tag

In python would look like so:

for sample in file('samples.txt'):
    fname, postfix = sample.split()
    output = file( "%s.new" % fname, 'wt')
    for line in file(fname):
        line = line.strip()
        if line.startswith(">"):
            line = line + postfix
        output.write("%s\n" % line)

You can also invert the situation to first preload your samples into a dictionary like so:

store = {}
for sample in file('samples.txt'):
    fname, postfix = sample.split()
    store[fname]=postfix

fname = "one.fasta"
postfix = store[fname]
output = file( "%s.new" % fname, 'wt')
for line in file(fname):
    line = line.strip()
    if line.startswith(">"):
        line = line + postfix
    output.write("%s\n" % line)

try this: with "Filename My identifier" file (asuming tab delimited)

cat Filenames.txt | while read LINE; do FNAME="$(echo $LINE | cut -d"\t" -f1 )"; ID="$(echo $LINE | cut -d"\t" -f2)"; awk -v code="ID" '{sub(/^>/, "$code", $0); print}' ${FNAME}.fasta ; done

I haven't tested though