"Roadrunners" was the name of the former IHL team that played in Phoenix, so that might not have been bad, but they still existed when the first iteration of the Winnipeg Jets came to town, so they couldn't exactly use it (probably could have if they'd bought off the Roadrunners for the name, but I guess they weren't willing to do that). They actually continued to exist for one season alongside the Coyotes, competing with them for fans, but it was kind of a disaster and they folded after that year. There were other teams that also used the Roadrunners name at various points in time, including the WHA, and a few years of revival in the ECHL in the late 2000s (the latter did not go very well, although they were affiliated with the Coyotes for a bit). The name was resurrected eventually when the Coyotes bought their AHL affiliate and relocated them to Tucson, and as of right now, the Tucson Roadrunners still exist (but there are some rumblings that they'll move to Reno).
"Scorpions" according to
one article is the name that finished second to "Coyotes" in the name-the-team vote. I can't find any other articles that claim that, but some other potential names are mentioned by several articles (including Mustangs, Outlaws, and Wranglers), so take that with a grain of salt. I wasn't paying attention in 1996, since I was only 10 years old at the time and wasn't watching hockey yet, and didn't even become aware that Phoenix got a hockey team until several years later, so it's not like I can say from personal experience what the buzz surrounding naming the team was like.