You should just check in the beginning of every iteration if platename is changed, and if it is, just reset numeration. Perhaps the following snippet would help you. Note that I not tested it

my $oldname; # here we will store previous name
foreach my $sam (@order) {
    # here is the current name
    my $platename = $save{$sam}{platename} || $save{$sam}{plateid};
    # if name is changed, reset n to 1
    $n = 1 unless $patename eq $oldname;
    if ( $save{$sam}{clone} =~ /BLANK|Water/i ) {
        print OUT
"$n,$save{$sam}{platename},$save{$sam}{well},,$save{$sam}{plateid}$sav
+e{$sam}{well}_BLANK,,,BLANK,,,,,,,,,,\n";
        $n++;
    }

    print OUT
"$n,$platename,$save{$sam}{well},$save{$sam}{case},$save{$sam}{plateid
+}_$save{$sam}{well}_$save{$sam}{clone},Homo sapiens,$save{$sam}{gende
+r},,$save{$sam}{vol},50,$save{$sam}{extmethod},,0,$save{$sam}{father}
+,$save{$sam}{mother},,$save{$sam}{source}\n";
    $n++;
    # store platename
    $oldname = $platename;
}
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