The $view object is usually available (along with other useful information) to the theme preprocess functions for the particular template. (Intro to preprocessor functions if you are unfamiliar http://drupal.org/node/223430). Within YOURTHEME_preprocess_views_view() in your template.php, the devel module's dpm() function will help you inspect the $vars handed to the template function.
YOURTHEME_preprocess_views_view(&$vars) {
dpm($vars);
}
Any new functions added to a theme's template.php require a theme registry rebuild (clearing cache). Inspect dpm's output to see if the $view display is available and then create a new keyed-item in $vars for usage in the tpl file.
Is it possible to access a Display title from within the views-view.tpl.php file?
Brian
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