If rindex has no matches, it returns -1. If substr gets a negative OFFSET, it "starts that far back from the end of the string". The correct approach here would be to test the result of rindex, and only modify if the number is non-negative:

if ((my $index = rindex( $name, q{.replaced})) > -1 ) {
    $name = substr $name, 0, $index;
}
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Note as well that you have an off-by-one error on your replacement, which I have fixed by adding '.' to your string.

Update: AnomalousMonk caught that the rindex was in the LENGTH argument, not the OFFSET argument.

If LENGTH is negative, leaves that many characters off the end of the string.