From poj's code:

my $name;
while ( my $para = <$PROTFILE> ) {
    # Remove fasta header line
    if ( $para =~ s/^>(.*)//m ){
      $name = $1;
    };
    ...
}
[download]

A quick and dirty and UNTESTED modification to do what I think you want:

my $name;
my %name_seen;  # fasta headers seen so far

FASTA_RECORD:
while ( my $para = <$PROTFILE> ) {
    # Remove fasta header line
    if ( $para =~ s/^>(.*)//m ){
      $name = $1;
      next FASTA_RECORD if $name_seen{ $name }++;
    };
    ...
}
[download]

Warning: The requirement to "... get rid of duplicate entries ..." is ambiguous. If there is more than one entry with the same header (i.e., $name), which is (or are, if there are more than two) the duplicate(s)? The first one? The last one? Etc. The code modification above ignores all entries with a given $name after the first one. Also, it might be wise to trim all leading/trailing whitespace from $name before any further processing whatsoever (also untested):
    $name = $1;
    $name =~ s{ \A \s+ | \s+ \z }{}xmsg;

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