This is convenient especially for modules with a “dynamic” mode, like mod_articles_category. It allows to also change the title dynamically depending on the menu item.

Copy the default.php file from your module's tmpl folder into /templates/your_template/html/name_of_your_module/. Towards the begining of the file (but after "defined('_JEXEC') or die;") add this

// Dynamically assign module title depending on the menu item
// Exclude some modules by adding them to the modexclude[] array
$modexclude = [];
$active = JFactory::getApplication()->getMenu()->getActive();
if ($active && !in_array($module->id,$modexclude)) :
 $module->title = JText::sprintf(htmlspecialchars($active->title));

The code will give dynamic titles to all instances of the plugin, but you can override specific ones by adding their ids to the modexclude[] array (separate with commas).