Assuming your contig names are as described without additional fields:

cat test
contig01 domain01.hmm
contig02 domain0434.hmm

cat test.fasta
>contig01
abcd
>contig02
efgh

join -1 1 -2 1 -o 2.1,1.2,2.2 <(sort -k1,1 test) <(cat test.fasta | tr "\n" " " | tr ">" "\n" | grep . | sort -k1,1) | awk '{print ">"$1"_"$2"\n"$3}' > test.annotated.fasta

cat test.annotated.fasta
>contig01_domain01.hmm
abcd
>contig02_domain0434.hmm
efgh

Given your datasets (and a more detailed posting of your question here), the following produces your requested output:

use strict;
use warnings;

my $file1 = shift;
my ( %hash, @F );

while (<>) {
    $hash{ $F[0] } = $F[1] if @F = split;
}

local $/ = '>';
push @ARGV, $file1;

while (<>) {
    print ">$F[0]_$hash{ $F[0] }\n$F[1]\n" if @F = split />|\n/ and $hash{ $F[0] };
}

Usage: perl script.pl foo.fa annotations.txt [>outFile.fa]

The last, optional parameter directs output to a file.

The script first creates a hash from the annotations' file, where the key is the identifier and its associated value is the annotation. While its reading the fasta file in chunks of records, it appends the annotation to the header and prints the record if it finds a matching identifier.

Hope this helps!