File::Basename comes 'for free' with perl (with the lower p), at least in recent installations. This gives you the advantage to write clean code, not to reinvent the wheel and avoid common pitfalls (which make the File::Basename solution simpler IMHO). And lets you not worry about portability, which may not be an issue today, but who knows?

OTOH, you're definitively right on the fast side:

#!/usr/bin/perl
use strict;
use warnings;
use Benchmark qw( cmpthese );
 
my $tempvalue = 'c:/reports/check/test.txt';
cmpthese( -5, {
   file_basename => sub { file_basename($tempvalue); },
   fast_and_simple => sub { fast_and_simple($tempvalue); },
});
 
 
sub file_basename {
   my $tempvalue = shift;
   require File::Basename; # Hits performance only once
   my ($name, $path) = File::Basename::fileparse($tempvalue);
   return $path . "design." . $name;
}
 
sub fast_and_simple {
   my $tempvalue = shift;
   my @split = split( '/', $tempvalue );
   my $file = pop @split;
   return join '/', @split, "design.$file";
}
 
__END__

                    Rate   file_basename fast_and_simple
file_basename    74479/s              --            -58%
fast_and_simple 175981/s            136%              --
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I dared to make the necessary modifications to your code in order to put it into the benchmark :)