A version showing some variations of technique (tested under Perl 5.8.9):

c:\@Work\Perl\monks>perl -e
"use warnings;
 use strict;
 ;;
 my @ListPeople = ListOfNames();
 ;;
 PERSON:
 for my $counter (0 .. $#ListPeople) {
   my $ar_person = $ListPeople[$counter];
   last PERSON if $ar_person->[0] eq '';
   print qq{$counter. What is my Name: @$ar_person \n\n};
   };
 ;;
 sub ListOfNames {
   my @LON;
   ;;
   $LON[0][0] = 'Tim';
   $LON[0][1] = 'O';
   $LON[0][2] = 'Tay';
   ;;
   $LON[1] = [ 'John', 'Fitz', 'Gerald' ];
   ;;
   $LON[2] = [ qw(Gerald Fitz John) ];
   ;;
   push @LON, [ '', 'not', 'here' ], [ 'Billy', 'Bob', 'Thornton' ];
   ;;
   return @LON;
   }
"
0. What is my Name: Tim O Tay

1. What is my Name: John Fitz Gerald

2. What is my Name: Gerald Fitz John
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The  ListOfNames() function could simply be written as:

sub ListOfNames {
  return
    [ 'Tim',   'O',    'Tay'      ],
    [ 'John',  'Fitz', 'Gerald'   ],
    [ qw(Gerald Fitz John)        ],
    [ '',      'not',  'present'  ],
    [ 'Billy', 'Bob',  'Thornton' ],
    ;
  }
[download]