Oyster cards are still there and are still an option, but no need to get one if you don't already have one and if you have a contactless credit card.
Since you need to tap in when you get on the train and tap out when you get off (unlike NYC where you don't need to tap out), you and your beloved should use separate cards, either separate credit cards or one Oyster and one CC
By the way you can use Google Wallet, Apple Pay etc and you can pay with a smart watch which saves the trouble of fumbling for cards in a busy station.
Forgot to mention is that there is a daily cap above which you ride for free. Check the TFL website (transport for London) for details.