t only shows up to users who are logged in, so even if you could change the title wouldn't be visible to others.
But as a workaround, here's some code you could put as a PHP block:
<?php
global $user;
if (user_access('edit own blog')) {
$items[] = l($user->name . "'s blog", "blog/" . $user->uid);
return theme_item_list($items);
}
?>
It should only show to logged in users who have the permission to edit a blog, and that link would only show to the specific users whose name appears in the link.