But let's say you want to replace 'Jane' (any case) with 'Mary' (same case). Here's one way of doing it:

#!/usr/bin/perl

use strict;
use warnings;

my $pat  = "jane";
my $repl = "mary";

while (<DATA>) {
    s/($pat)/$1 ^ $pat ^ $repl/eig;
    print;
}

__DATA__
jane janE jaNe jaNE
jAne jAnE jANe jANE
Jane JanE JaNe JaNE
JAne JAnE JANe JANE



mary marY maRy maRY
mAry mArY mARy mARY
Mary MarY MaRy MaRY
MAry MArY MARy MARY
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Abigail