in reply to
Regex to find repeated patterns
Hmmm, as Corion has pointed out, you'll get much better response by showing what you have tried, and in what way it fails.
That being said, does this code do what you are looking for?
my $str = "*L*Name1*L*Name2*L**D*Place1*D*Place2*D**L*Name3*L*";
my @names =$str =~ m/\*L\*(\w+)/g;
$str =~ s/\*L\*$names//;
print "Modified string = $str\n";
Name1 Name2 Name3
Modified string = *L*Name2*L**D*Place1*D*Place2*D**L*Name3*L*