The WordPress default menu functions offers a great many features and options, some of which can be difficult to modify without delving into the code itself. For example, if a theme author chooses to turn “on” the “show_home” option in the default menus such as Twenty Twelve does in its functions.php template file with this code (as of this writing):

/**
 * Makes our wp_nav_menu() fallback -- wp_page_menu() -- show a home link.
 *
 * @since Twenty Twelve 1.0
 */
function twentytwelve_page_menu_args( $args ) {
	if ( ! isset( $args['show_home'] ) )
		$args['show_home'] = true;
	return $args;
}
add_filter( 'wp_page_menu_args', 'twentytwelve_page_menu_args' );

Note line 194 is turning on the show_home option. If you have a look at the WordPress codex article for the wp_page_menu function you can read more about other menu options. To change the default “Home” text to something else, simply replace the word true with a word or phrase of your own choice (remember to place this new “Home” name in quotes).

Now, the best way to actually do this would be via a Child-Theme. All you need to do is create a simple Child-Theme and add a functions.php template file with a similar function as the one used in Twenty Twelve itself. Something like this would work:

/**
 * Makes our wp_nav_menu() fallback -- wp_page_menu() -- show a home link named "Bacon".
 */
function twentytwelve_child_theme_page_menu_args( $args ) {
	if ( ! isset( $args['show_home'] ) )
		$args['show_home'] = "Bacon";
	return $args;
}
add_filter( 'wp_page_menu_args', 'twentytwelve_child_theme_page_menu_args' );

Note the two differences: the function name; and, on line 6 the show_home option now reads "Bacon" instead of true.

This method will work with any theme that has turned on the show_home option in this fashion. The Twenty Twelve theme was used as an example as this post was inspired by this WordPress Support forum thread.

You might want to read this article as a reference for creating a Child-Theme as starting point, or a refresher if you are familiar with how to create a Child-Theme.