You can accomplish this functionality nicely using the Entity API module's metadata wrapper and hook_user_view(). Add a dependency to Entity API in your module's .info file and then the code could look something like the following (assuming you want to set the title to the user's full name and you have fields called field_first_name and field_last_name):
/**
* Implements hook_user_view().
*/
function MYMODULE_user_view($account, $view_mode, $langcode) {
// Set the page title of the user profile page to the user's full name.
$wrapper = entity_metadata_wrapper('user', $account);
$first_name = $wrapper->field_first_name->value();
$last_name = $wrapper->field_last_name->value();
if ($first_name && $last_name) {
drupal_set_title($first_name . ' ' . $last_name);
}
}