Drupal - How to add db_select condition by using two concatenated fields?

You can try something like the following. You build the name with a small sql expression and then can use it within the where clause.

$select = db_select('people_table', 'p');
$select->addField('id');
$select->addExpression("CONCAT(p.first_name, ' ', p.last_name)", 'full_name');
$select->condition('p.full_name', $some_name, 'LIKE');
$results = $select->execute();