If you want to alter the title tag that is generated by Joomla, you can change it in

libraries/joomla/document/html/renderer/head.php

This is the file that is called by ...

<jdoc:include type="head" />

in the index.php of your template file.

For example, if you want to add your site name at the end of the title, add the text in bold in the following code line...

$strHtml .= $tab.'<title>'.htmlspecialchars($document->getTitle()).' - Your Site title here</title>'.$lnEnd;

Instead of hard-coding the "Your Site title Here", you can retrieve the value set in the Admin global configuration by something like ...

global $mainframe;
$yoursitetitle = $mainframe->getCfg('sitename');

Note that altering head.php is considered altering the core Joomla files. This is not ideal as an upgrade of Joomla version will wipe out the modification if you do not do a code comparison and merge. So a better way of doing this is to code it as dictated by Joomla best practice to use extensions and plugins.

You would create a System Plugin with code that looks like ...

function onAfterDispatch() {
global $mainframe;

$document = & JFactory::getDocument();
$docType = $document->getType();
// Only mod site pages that are html docs (no admin, install, etc.)
if ( !$mainframe->isSite() ) return;
if ( $docType != 'html' ) return;

$document->setTitle($document->getTitle() . ' - ' . $mainframe->getCfg('sitename'));
return true;
}

See tutorial linked here for detailed steps for creating a Joomla Plugin.

If you do not want to write a plugin, you might want to consider the Tag Meta plugin.