Have you considered using a hash? This code meets both of your stated requirements:

sub file_name {
  my %args;
  @args{qw/client_number MM DD S/} = @_;

  for (keys %args) {
    defined($args{$_}) or die "\$$_ not defined";
  }

  local $";
  "I@args{qw/client_number MM DD S/}";
}
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You could even put the for loop in a separate subroutine and call it from all your subroutines where you want to verify the arguments.