my $name = 'Smith';
my $st = $db->prepare( qq| SELECT * FROM mytable WHERE customer = '$name'; | );
$st->execute or die $DBI::errstr;

# or with placeholders
my $name = 'Smith';
my $st = $db->prepare( q| SELECT * FROM mytable WHERE customer = ?; | );
$st->execute($name) or die $DBI::errstr;