How to get a notification when the plugin is installed?

I do not recommand using is_plugin_active() because if you rename your plugin directory which is done sometimes for security needs you’re screwed.

If I were you I’d look into plugin you want to detect and select a core class or a core function of the plugin and test it with if(class_exists('name_of_the_class')) or if(function_exists('name_of_the_function')).

Hope this will help, that how I proceed.