We liked the Sidestep system in 3.1 which was called the Free Step Dodge because it was dodging by using the Free Step system. In addition, we wanted to pave a new direction for the competitive community of Dead or Alive and start a brand new website fresh, so the unofficial tagline at the time was "Stepping into a new direction" (You'll also notice my signature relates to stepping as well). It was considered an advanced technique to Dead or Alive that we wanted to merge with the desire of being an advanced site for the Dead or Alive series.
Both Virtuapai and myself do not like all the attention the Ninjas (especially Ryu and Kasumi) receive for the game - we're personally a fan of the non-ninjas like Tina, Lei Fang, Jann Lee, and Bass. Yes, it was going against an already established marketing niche, but we weren't specifically looking for a "DOA" fansite in the same vein as the others. We accept casual discussion and fan appreciation here, we just don't have it as the focus of the site. In that regard, names like Izuna Otoshi, Izuna Drop, and Mugen Tenshin were disregarded. Naming it after Hayabusa or anything related to him could also give off the impression that it would be a DOA/Ninja Gaiden site, which again wasn't the focus. Since no other moves are synonymous with DOA like Shoryuken is with Street Fighter, barring "Dragon kick" from Jann Lee but it being too vague caused its demise. We also didn't want to bring more heat to the most glaring complaint of the game: The Defensive Hold. So we couldn't use that as well.
We were additionally paying homage to 8WayRun as well as Jaxel was a good friend of Hubbs and myself through our offline tournaments, and would go on to aid us in converting the forums to XenForo.
Lastly, it's because I said so; the community makes the name, the name doesn't make the community. If the community continues to post here then Google and other browsers would eventually start linking here with Dead or Alive search queries. This site is meant to spread through word of mouth much like we want the competitive community to grow through the grassroots community.