You won't be able to determine the intended output until you have read the entire input file into memory and have gone over all the records to check the numeric values associated with names in the fourth field. Maybe something like this:

#!/usr/bin/perl

use strict;
use warnings;

my @records;
my %max;
while (<DATA>) {
    my @fields = split;
    my ( $number, $name ) = ( $fields[3] =~ /^(\d+),(\w+)/ );
    if ( ! $number or ! $name ) {
        warn "Line $.: unexpected input ignored: $_";
        next;
    }
    $max{$name} = $number
        unless ( exists( $max{$name} ) and $max{$name} >= $number );
    push @records, { name => $name, data => $_ };
}

for my $rec ( @records ) {
    my $name = $rec->{name};
    my $max = $max{$name};
    my $flag = ( $max == 1 ) ? 'single' : 'end';
    $rec->{data} =~ s/(\s)$max,$name,/$1$flag,$name,/;
    print $rec->{data};
}

__DATA__
62556    63635    y    1,andrew,JJ113954
63868    63897    h    1,morgan,JJ113955
68766    69005    j    2,morgan,JJ113955
81099    81630    y    1,flintoff,JJ113952
126185    126699    s    1,austin,JJ113956
135356    135449    3    1,peter,JJ113952
135588    136297    8    2,peter,JJ113952
158146    158367    i    3,peter,JJ113952
441474    441538    b    9,catherine,JJ029490
442666    442843    9    8,catherine,JJ029490
445778    445905    0    7,catherine,JJ029490
446059    446273    l    6,catherine,JJ029490
450319    450379    f    5,catherine,JJ029490
[download]

(updated to add a condition for skipping lines that don't match /\d+,\w+/ in fourth field-- it pays to be careful...)

In the for loop, the $rec->{data} =~ s/.../.../ will do nothing on the lines that don't contain the max value for a given name, because the regex won't match. For lines that contain a max value, the replacement will be either "single" or "end" depending on what the max value is.

In order to read from a file name that you put on the command line (i.e. in @ARGV) when you run the script, just remove DATA from while(<DATA>) (and leave off the __DATA__ section at the end) -- there's no need to explicitly open a file whose name is provided via @ARGV.