You can use “get_avatar” function to display avatar in menu with user name. Please try code given below:
add_filter( 'wp_nav_menu_objects', 'my_dynamic_menu_items', 10 );
function my_dynamic_menu_items( $menu_items ) {
foreach ( $menu_items as $menu_item ) {
if ( strpos($menu_item->title, '#profile_name#') !== false) {
$menu_item->title = str_replace("#profile_name#", wp_get_current_user()->user_login .' '. get_avatar( wp_get_current_user()->user_email, 50), $menu_item->title);
}
}
return $menu_items;
}