If I understood the question correctly, you can use something like this to remove the default buttons from the WP tinyMCE.
// Remove TinyMCE Default Button
function myplugin_tinymce_buttons( $buttons ) {
//Remove the text color selector
$remove = 'blockquote'; //default blockquote button
//Find the array key and then unset
if ( ( $key = array_search( $remove, $buttons ) ) !== false )
unset( $buttons[$key] );
return $buttons;
}
add_filter( 'mce_buttons', 'myplugin_tinymce_buttons' );
to know what is the name of the element you need to use your browser dev tools. Simply highlight the element and see the class. It will be also the name. For example:
where to see the name of the element