reduce

use feature qw(say);
use strict;
use warnings;

{
    my @names;  # keeps the same order of the lines
    my %lines;  # names and numbers

    read_file('file1', \@names, \%lines);
    read_file('file2', \@names, \%lines);
    for my $name (@names) {
        say $name, " ", join " ", @{$lines{$name}};
    }
}

sub read_file {
    my ( $fn, $names, $lines ) = @_;
    open ( my $fh, '<', $fn ) or die "Could not open file '$fn': $!";
    while( my $line = <$fh> ) {
        chomp $line;
        next if $line !~ /\S/;  # skip empty lines
        my ( $name, $number ) = $line =~ /^(.*)\s+(\d+)\s*$/;
        push @$names, $name if !exists $lines->{$name};
        push @{$lines->{$name}}, $number;
    }
    close $fh;
}