For subsequent transactions, they send the name/number only.
I recently had a new CC issued, so new expiry date & CVV, but same number. Some places I use for recurring payments sent me emails warning that my CC was about to expire and that I should update my stored details, others did not. Those that did, I updated, those that didnt I waited for them to complain before updating anything. Lotto never noticed, neither did 2degrees.