User Name in Header

You would need to use the tml_title filter to change the title according to the action:

function my_custom_tml_title( $title, $action ) {
    if ( 'login' == $action && is_user_logged_in() ) {
        $user = wp_get_current_user();
        $title = sprintf( 'Welcome, %s', $user->display_name );
    }
    return $title;
}
add_filter( 'tml_title', 'my_custom_tml_title', 10, 2 );

Hello jeff where should i put the script?
I’ve put it in theme-my-login-custom.php file.
But did not show as well in Header.

I recommend placing all TML-related code in wp-content/plugins/theme-my-login-custom.php.

Hi Jeff,
I’ve made it on theme-my-login-custom.php :

https://text-share.com/view/11a6285b

but after login the user name still does not appear
Just Logout and Your Profile only in the header.
Are there any settings I missed?

You have all of the code from theme-my-login.php there – that doesn’t belong. Also, how are those items added to the header? Is it a wp_nav_menu()?