Alma enacted the covenant of baptism with all who had come to the place of Mormon. Had these people been previously baptized? We cannot know. What we can know is that Alma instituted a second function of baptism as an entry covenant. Even had they been baptized previously, the new baptism enacted their entry into the new covenant. It is the same in our modern experience. Regardless whether a convert was previously baptized, they are baptized again, not simply for the cleansing, but for the entrance into the new covenant of the restored gospel.
Verse 17 introduces the idea that this new, separated, people were “called the church of God, or the church of Christ.” While modern readers might see a difference in the terms “God” and “Christ”, Alma did not. He taught that which Abinadi had taught, which was that Jehovah himself (who is God), would come down to earth to be the Messiah. Thus, the terms were intended to be equivalent, two ways to say the very same thing.
The idea of “church” is also a new innovation. In both the Hebrew and the Greek, the word behind the translated “church” means an assembly or congregation. For the Hebrews, it meant the faithful, and in the Greek it defined the group who gathered together and believed in the gospel of Christ. Alma’s use of the term is more similar to the Greek, and perhaps similar again in that it was the beginning concept that would lead to the more specific definition of a church as a separate body of believers inside of the larger community. That was certainly what they had done in the land of Mormon, and it will happen after Alma arrives in Zarahemla. It will likely happen through his influence since it was a change from the way religion had been administered up to that point.