I have a Drupal Menu which I created through the interface. I wish to add an entry which says
Hi, John Doe
Where "John Doe" is a link to the User's profile page. I would like to do this programmatically or if it can be done through the interface then that would be great.
You cannot add HTML-ified items to the menu. Menu-items are always wrapped in an anchor tag and will filter out HTML. Changing this behaviour is technically possible, but will cause a lot of unknown side-effects.
What you want, is either a simple theme override, or a custom block (potentially without a title and with some other bullets).
You can create a block with hook_block or by simply typing the HTML, with some PHP into a new block, using the PHP-input filter. This last option is quick, but is discouraged by many people for performance and "good practices" reasons: you should not store php in your database.
EDIT: After comment about "just the name":
To insert "just the name" you simply need to create module with a hook_menu.
global $user;
$items['path/%uid'] = array(
'title' => $user->name,
'description' => 'description',
'page callback' => 'drupal_get_form', //Fill in the callback here: function that renders the page content.
'page arguments' => array(''),
'access callback' => '',
'access arguments' => array(''),
'weight' => 0,
'menu_name' => 'Navigation',
'type' => MENU_NORMAL_ITEM,
);
Is about what you want.
