This is actually for Page Header output, but the same applies to the Browser Title. I've had this situation occur most frequently with 3rd party components. Joomla stores these values when you specify them in the menu item, but it's up to the component whether or not they're used. Below is the code I've added to my components, and sometimes to the template overrides. If you're not familiar with template overrides, you should read How to override the output from the Joomla! core first.
Put this code before any other HTML code in the template override file. It checks to see if you've specified to show the page headings or not, and if so, it will use that, otherwise it will use whatever the menu title is.
<?php if ($this->params->get('show_page_heading',1)) : ?>
<h1><?php echo $this->params->get('page_heading') ? $this->params->get('page_heading') : JFactory::getApplication()->getMenu()->getActive()->title; ?></h1>
<?php endif; ?>
To see how Joomla does it by default, look at
<div class="item-page<?php echo $this->pageclass_sfx?>">
<?php if ($this->params->get('show_page_heading', 1)) : ?>
<h1> <?php echo $this->escape($this->params->get('page_heading')); ?> </h1>