Izumi: "Revenge-Tan," due to her mental state after her boyfriend is killed in battle.
Foreshadowing: For April Fools 2013, age made spoofs of various pieces of official and promotional artwork from other anime series (eg. The poster for the second of the two Puella Magi Madoka Magica recap movies). One of them was a spoof of the cover for the first volume of the Oreimo light novel, with Kirino and Kyosuke replaced with Yui and Yuuya, and re-titled "There's No Way My Little Sister Can Be This Samurai!". This was a hint at their blood relation as half-siblings, which was later revealed in the visual novel.
I Knew It: One poster on Animesuki speculated that Yuuya and Yui are half siblings. This was confirmed by the VN.