As to the origins of the show's name, Kamen Rider Revice, he came up with the Rider names by thinking of having a gimmick in which the two Rider names will form the show's titles. Vice was decided first as it means "a bad habit" or "immoral", making it the perfect name for the devil. As to the other half, which is Revi, it took a while to find a suitable name that will compliment "i" or "vi" before they landed with the Hebrew word "levi", which means "to connect" and there's also the monster called Leviathan. By combining the two words, Revice means "to connect with the devil".
As to how they ended up as the main animal motif for the Kamen Riders, this has something to do with the idea of pulling something out of the body with a stamp. Mochizoki brought up "biological genes" as a motif idea. That said, it evolved into the genetic information of an organism that accumulated in the human body is taken out by the stamp and is enlarged. They needed something relatively strong for the basic form, and it was unanimously decided that no one was as strong as the tyrannosaurus rex. Plus, there's no Kamen Rider based on a T-Rex, making it a fresh and nice concept.
Finally, the timeline of Kamen Riders Revi and Vice's movie appearances also confirmed. Their appearance in their own movie that aired after Superhero Senki takes place after episode 3, and can be labeled as "episode 3.5".
[via Nihon Hero]