Example of using civicrm_alterReportVar hook

myextension.php

<?php

/**
* Implements hook_civicrm_alterReportVar().
 */
function myextension_civicrm_alterReportVar($varType, &$var, &$reportForm) {
  if ($varType === 'columns') {
    $var['civicrm_value_extension_tng55'] = [
      'fields' => [
        'extension_tng55_title' => [
          'title' => ts('Extension Title'),
          'dbAlias' => "civicrm_value_extension_tng55.title",
        ],
      ],
      'filters' => [
        'extension_tng55_title' => [
          'title' => ts('Extension Title'),
          'dbAlias' => "civicrm_value_extension_tng55.title",
          'type' => CRM_Utils_Type::T_INT,
          'operatorType' => CRM_Report_Form::OP_MULTISELECT,
          'options' => [
            1 => 'title 1'
          ],
        ],
      ],
    ];
  }
  if ($varType === 'sql') {
    if (isset($reportForm->getVar('_params')['fields']['extension_tng55_title'])
      || isset($reportForm->getVar('_params')['extension_tng55_title_op'])) {
      $from = $var->getVar('_from');
      $from .= "
          LEFT JOIN civicrm_value_extension_tng55
          ON (civicrm_value_extension_tng55.entity_id = contribution_civireport.id)
      ";
      $var->setVar('_from', $from);
    }
  }
}