Displaying Logged-In User Name and avatar in WordPress Menu

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;
}