Nice and valid point which needs great consideration. Thanks to bring it to our attention.
Did you try by changing the Page name to your website name itself? If not could you please try it once if it works. Meantime I will looking to the code and if it requires any conditional statement than will update and push it to the store.
[ Here is the fix ] --------------------------------------------------------------------------------
open file q2am-front-page-custom.php from q2am-front-page plugin directory
at line #95 fine below code
Find
/* TRANSFER LANGUAGE STRINGS */
$lang_page_title = qa_lang_html('q2am_front_page_lang/page_title');
and Replace with below
/* TRANSFER LANGUAGE STRINGS */
$url = 'http://' . $_SERVER['SERVER_NAME'] . $_SERVER['REQUEST_URI'];
$lang_page_title = ($url == qa_opt('site_url')) ? '' : qa_lang_html('q2am_front_page_lang/page_title');
This will check if you have set the Front Page as a home page than it will remove the Front Page title and will only display the Site Name