What was the church first called and why were believers then called Christians?
 
The way was something the disciples spoke of i.e., the gospel. This way was spoken of by John, by Jesus - it is what Jesus spoke of himself and what others spoke of him.
 
Luke 20:21 Then they asked Him, saying, “Teacher, we know that You say and teach rightly, and You do not show personal favoritism, but teach the way of God in truth”
 
John the baptizer preceding Jesus (Jn.1:23) said: “I am 'The voice of one crying in the wilderness: “Make straight the way of the Lord,” 'as the prophet Isaiah said.”
 
John 14:4-6 And where I go you know, and the way you know.” Thomas said to Him, “Lord, we do not know where You are going, and how can we know the way?”
Jesus said to him, “I am the way, the truth, and the life. No one comes to the Father except through Me.”

From Jesus explaining he is the way and those following him and telling others the way to be saved the name was made known throughout the land.

Acts 9:1-2 “Then Saul, still breathing threats and murder against the disciples of the Lord, went to the high priest  and asked letters from him to the synagogues of Damascus, so that if he found any who were of the Way, whether men or women, he might bring them bound to Jerusalem.” Also used in Acts 16:17.
 
Acts 11:26 “And the disciples were first called Christians in Antioch.” Stephen chosen by the apostles was from Antioch (Acts 6:5). After the death of Stephen (Acts 11:19-20) the disciples were scattered and went to Phoenicia, Cyprus, and Antioch preaching to the Jews who spoke Greek.
Acts 11:21-22 And the hand of the Lord was with them, and a great number believed and turned to the Lord. Then news of these things came to the ears of the church in Jerusalem, and they sent out Barnabas to go as far as Antioch.”

Acts 11:25-27 Barnabas departed for Tarsus to seek Saul. And brought him to Antioch. “So it was that for a whole year they assembled with the church and taught a great many people. And the disciples were first called Christians in Antioch. And in these days prophets came from Jerusalem to Antioch.”
This city in Syria became a main hub for Christianity

They had changed their name in this area for some reason that made them think of them as more in relationship to Jesus and had been named as those who were like him, following in his steps. Three of Paul's missionary journeys began in Antioch. revisiting this city on his first mission tour Acts 14:21) .

At the church council in Jerusalem the apostles and elders, with the whole church, sent men to Antioch with Paul and Barnabas (Acts 15:22). Acts 15:35 “Paul and Barnabas also remained in Antioch, teaching and preaching the word of the Lord, with many others also.”

Still after this they were known as the way throughout the land. Acts 19:8-9 “And he went into the synagogue and spoke boldly for three months, reasoning and persuading concerning the things of the kingdom of God.  But when some were hardened and did not believe, but spoke evil of the Way before the multitude, he departed from them and withdrew the disciples, reasoning daily in the school of Tyrannus.”

Acts 24:14 Paul before Felix spoke: “But this I confess to you, that according to the Way which they call a sect, so I worship the God of my fathers, believing all things which are written in the Law and in the Prophets.”
V.22 “But when Felix heard these things, having more accurate knowledge of the Way, he adjourned the proceedings and said, “When Lysias the commander comes down, I will make a decision on your case.”

They were called Christians by those outside and inside and called themselves saints inside the church as well.
Both names were used in the land. Acts 26:28 Then Agrippa said to Paul, “You almost persuade me to become a Christian.”

1 Peter 4:16: “Yet if anyone suffers as a Christian, let him not be ashamed”

We know the name Christian became popularized throughout history mainly to distinguish who the church preaches, follows and serves.