Well, I didn't realize your input files were all newline free.. Should have read the question more closely.

In that case, Bioperl is even better...

use Bio::SeqIO;
while (my $fname = shift) {
   ## raw is one seq per line (no newlines)
   my $in  = Bio::SeqIO->new(-file => "$fname",
                            '-format' => 'raw');
   $fname =~ s{\.txt}{}' # strip .txt
   my $outfile = $fname . ".fa";
   my $out = Bio::SeqIO->new(-file => "> $outfile" ,
                           '-format' => 'fasta');
 
   ## Do the conversion
   while ( my $seq = $in->next_seq() ) {
       $seq->display_id($fname); # Add a name
       $out->write_seq($seq);
   }
}
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Run it in the same way, with an argument of *.txt