Use substr to extract and replace:

my $oldfile = "name_0009";
my $num = substr($oldfile, -4);
++$num;
my $newfile = substr($oldfile, 0, -4) . $num;
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Or use the lvalue form to simplify things:

my $oldfile = 'name_0009';
substr(my $newfile = $oldfile, -4)++;
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