The "standard" way to compute the longest left-anchored common substring would be to compare character for character of both strings until they differ. However, in Perl it's relatively cumbersome (compared to C for example) to access a single character in a string (via the substr builtin), so this approach is quite slow (even for rather short strings like your sample).

For comparison, here's the results of a quick benchmark, so you'll actually appreciate the performance of the XOR method suggested by Corion:

#!/usr/bin/perl

use Benchmark qw(cmpthese);
use Inline C;

my $s1 = '/home/usernames/doejohnwilson';
my $s2 = '/home/usernames/doejanemary';

cmpthese(-1, {
    'standard' => sub {
        my $pos = 0;
        $pos++ while substr($s1, $pos, 1) eq substr($s2, $pos, 1);
        my $result = substr($s1, 0, $pos);
        # die unless $result eq "/home/usernames/doej";
    },
    'fancy-XOR' => sub {
        my $common = $s1 ^ $s2;
        my $common_length = 0;
        if ($common =~ /^(\x00+)/) {
            $common_length = length $1;
        };
        my $result = substr($s1, 0, $common_length);
        # die unless $result eq "/home/usernames/doej";
    },
    'standard-XS' => sub {
        my $common_length = left_anchored_common_substr_len($s1, $s2);
        my $result = substr($s1, 0, $common_length);
        # die unless $result eq "/home/usernames/doej";
    }
});

__END__
__C__
int left_anchored_common_substr_len(char* s1, char* s2) {
    int c = 0;
    while (*s1++ == *s2++) { c++; }
    return c;
}
[download]

Results:

                 Rate    standard   fancy-XOR standard-XS
standard     109227/s          --        -77%        -92%
fancy-XOR    468114/s        329%          --        -64%
standard-XS 1291788/s       1083%        176%          --
[download]

Update: added an XS routine (via Inline::C) that implements the aforementioned "standard" approach in C.