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 }++;
    };
    ...
}