#!/usr/bin/perl -w
use strict;

my @files = qw(file1.dat file2.dat);
my %hash;

foreach my $file (@files)
{
   open (FILE, "<", $file) || die "can't open $file $!";
   while (<FILE>)
   {
      next if /^\s*$/;
      chomp;
      my ($name,@tokens) = split(/,/,$_);
      $name =~ s/_.*$//; #delete trailing _blah in name
      push @{$hash{$name}},@tokens;
   }
}

foreach my $name (sort keys %hash)
{
   print "$name  @{$hash{$name}}\n";
}

__END__
prints:
Bbbb  3333 4444 23 45
Cdd  3444 3444 24.45
Zddd  345 456 34 456.4

file1.dat:
Bbbb,3333,4444
Cdd,3444,3444
Zddd,345,456

file2.dat
Bbbb_rf1,23,45
Cdd_rf2,24.45
Zddd,34,456.4