You can still use a hash, but you have to check whether the key already exists before setting the value.

#!/usr/bin/perl
use warnings;
use strict;

my %seen;
while (<DATA>) {
    my ($name, $count) = split;
    $seen{$name} = $count unless exists $seen{$name};

}
print "$_ $seen{$_}\n" for keys %seen;

__DATA__
nick 5
nick 10
nick 20
john 78
erik 9
erik 12
[download]

If you want to store the values in an array, use

    push @keep, $_ unless $seen{$name}++;
[download]

Or, you can print the lines directly:

    print unless $seen{$name}++;
[download]