Nah, he probably cannot be sued for using “Baptist” because anyone can use that. Look at Westboro. This is probably why they choose “Baptist”
Looking at the "church" website, it appears that this group was part of the SBC at one time, but left because they decided they were "moderate Baptists". They are now part of a group called "Cooperative Baptist Fellowship" - basically a bunch of apostate Baptist churches who want to have their religion evolve with the culture, rather than adhere to timeless Biblical principles.