Based on the way my On twins have been behaving, it looks like the tamagotchi on the left does indeed get the first name, which is further aided by it the primary actor in animations and games, while the tamagotchi on the right gets the second name. Thus, Creamitchi is the yellow one and Puddingitch is the white one. Theme-wise, this still works as cream is usually a pale yellow and the typical pudding is usually vanilla and thus white. Those names are so cute XD I just named my twins Barbratchi and Bethanytchi.
The On treats the twin, the second named, almost as a tag along companion - paralleling park animations at locations with the encountered residents - which shows that the On hasn't really adapted to the concept of having two focal actors. This is a similar case with the V5 where a family of tamagotchis could be raised - usually three children and their parents - but the parents only really came into contact as game actors and in token sprites, while the oldest child was used exclusively for games. The V5.5 did allow a choice of what sibling played the game and thus made it a bit more like there were three genuine tamagotchis on the same device. However, in both the V5 and V5.5, the children eat together and did all other activities together, thus balancing the focus. Enjoy your free trivia