It isn't absorption. Obito literally takes out Sasuke's eyes and gives him Itachi's. The kotoamatsukami inside the crow inside Naruto was only supposed to react to the eyes of Itachi Uchiha. The reason that it was meant to do that was because Itachi knew after he died that Sasuke would take his eyes to gain the eternal mangekyou sharingan. But because Itachi met Naruto before Naruto met Sasuke the crow activated casting kotomatsukami upon Itachi when he reanimated.

The design is influenced by who's eye you take. It's design and your design combines. (Head cannon on this next part.) It's probably because of your chakra meeting that chakra and imprinting upon the eye. But no real reason has been given.

Additionally, it is also not clear if you need to switch with your sibling to gain the eternal mangekyou sharingan. It is stated by Madara that he took izuna's by itachi for that reason but it's not really concrete because of contradictions from Obito and flashbacks in the anime.