King Mosiah gathered the people of Nephi and of Zarahemla
2 Now there were not so many of the children of Nephi, or so many of those who were descendants of Nephi, as there were of the people of Zarahemla, who was a descendant of Mulek, and those who came with him into the wilderness.
(who were the descendants of Nephi and Mulek, respectively)
5And it came to pass that Mosiah did read, and caused to be read, the records of Zeniff to his people; yea, he read the records of the people of Zeniff, from the time they left the land of Zarahemla until they returned again.
and read to them the record of Zeniff
and the record of Alma, from the time they left the land of Zarahemla until the time they returned again.
When Mosiah finished reading the records, the people were filled with wonder, amazement,
exceedingly great joy,
10 And again, when they thought of the immediate goodness of God, and his power in delivering Alma and his brethren out of the hands of the Lamanites and of bondage, they did raise their voices and give thanks to God.
Then they thought about their sinful and polluted Lamanite brethren. 
12And it came to pass that those who were the children of Amulon and his brethren, who had taken to wife the daughters of the Lamanites, were displeased with the conduct of their fathers, and they would no longer be called by the names of their fathers, therefore they took upon themselves the name of Nephi, that they might be called the children of Nephi and be numbered among those who were called Nephites.
The people of Amulon were so upset with their fathers for taking the Lamanite daughters that they began to call themselves Nephites.
When Mosiah finished reading to the people, Alma began to speak.
17And it came to pass that after Alma had taught the people many things, and had made an end of speaking to them, that king Limhi was desirous that he might be baptized; and all his people were desirous that they might be baptized also.
After Alma stopped speaking, King Limhi and his people wanted to get baptized.
18 Therefore, Alma did go forth into the water and did baptize them; yea, he did baptize them after the manner he did his brethren in the waters of Mormon; yea, and as many as he did baptize did belong to the church of God; and this because of their belief on the words of Alma.
So Alma baptized them in the waters of Mormon, and they became members of the church of God.
21 Therefore they did assemble themselves together in different bodies, being called churches; every church having their priests and their teachers, and every priest preaching the word according as it was delivered to him by the mouth of Alma.
22 And thus, notwithstanding there being many churches they were all one church, yea, even the church of God; for there was nothing preached in all the churches except it were repentance and faith in God.
There were now so many members of the church of God that they had to divide them into different bodies, which they called churches.
So there were now seven churches in the land of Zarahemla, and whoever wanted to belong to the church of Christ or of God joined the churches of God.
And they were called the people of God and the Lord poured his spirit on them.