Displaying a Welcome Message to a Woocommerce User

This is not a WooCommerce question. Once the user is registered you use WordPress functions to verify whether the user is logged in and to retrieve the user’s info. Assuming you are saving the user info correctly, then this should show a user’s first name to the user, and a generic message to a non-logged-in user.

if ( is_user_logged_in() ) {
    $current_user = wp_get_current_user();
    echo 'Welcome, ' . $current_user->user_firstname . '!';
} else {
    echo 'Welcome, visitor!';
}

See the Codex for references:

is_user_logged_in()
wp_get_current_user()