use Data::Dumper;

@Names=qw(A B C);
@FullRecord=qw(A_1 D_4 C_3 F_6 B_2);

@name_presence{@Names} = ();
@DesiredRecord
    = grep { exists $name_presence{(split /_/)[0]} } @FullRecord;

print Dumper \@DesiredRecord;
__END__
$VAR1 = [
          'A_1',
          'C_3',
          'B_2'
        ];
[download]

use strict;
use warnings;

my %Names = (A => 1,  B => 1, C => 1);
my %FullRecord = (A_1 => 1, D_4 => 1, C_3 => 1, F_6 => 1, B_2 => 1,);
my @DesiredRecord = ();

foreach my $el (keys(%FullRecord)) {
  my @SplitArray=split(/\_/,$el);
  unshift(@DesiredRecord, $el) if exists $Names{$SplitArray[0]};
}
print "@DesiredRecord";
[download]

the solution presented by kyle is somehow idiomatic, this would be a good choice. You can use an alternative form w/regular expressions in order to solve a more complicated pattern problem.

The regex-form of kyle's solution would be like:

 ...
 my @Names      = qw'A B C';
 my @FullRecord = qw'A_1 D_4 C_3 F_6 B_2';

 # prepare temporary dictionary
 my %h; @h{@Names} = (); 

 my @DesiredRecord =
     grep exists $h{ [/^([^_]+)/]->[0] },
        @FullRecord;
    
 print "@DesiredRecord\n";
 ...
[download]

Regards

mwa

my @array1 = qw/a a b b c c d d/;
my @array2 = qw/        c c d d e e f f g g/;
my @array3 = ();
my %filter = ();

foreach (@array1) {
  $filter{$_} = 1;
}
foreach (@array2) {
  if (exists($filter{$_}) && 2 == ++$filter{$_}) {
    push(@array3,$_);
  }
}
print join(' ',@array3);
[download]

foreach $el (@Fullrecord) {
    @splitarray=split(/\_/,$el);
    foreach $nameel (@Names) {
        push (@DesiredRecord, $nameel) if ($nameel eq $splitarray[0]);
        }
}
[download]