How to set a different page title and another headline - for a page (plugin)?

Question

Writing a plugin, setting the h1 title by:

$qa_content['title'] = 'plugin name';

However, I want the page title (the title that the browser shows on top and can be seen in the bookmark) to be different.

How to achieve that from within a plugin? qa_register_plugin_module('page', ...

I have tried: $qa_content['site_title'] = 'Other name';

But it does not work.

With a theme I know I could override public function head_title() at: $this->output('<title>'.$headtitle.'</title>');

Comments

I probably can help if I know but can you please explain with some screenshots? Where and what exactly you want to do.