Soon after Pentecost (Acts 2), the priests, temple leaders and Sadducees started to persecute the Messianic, who preached that Jesus (Acts 4:1-22) was the Messiah (Christ) in Jerusalem.

And there arose on that day a great persecution against the church in Jerusalem, and they were all scattered throughout the regions of Judea and Samaria, except the apostles. ... Saul was ravaging the church, and entering house after house, he dragged off men and women and committed them to prison. Now those who were scattered went about preaching the word. -- Acts 8:1,3-4 (ESV)

This first generation of disciples often identified themselves as the Way. This name possibly came from the Messiah whom they followed, who initially identified himself as:

“I am the way, and the truth, and the life. -- John 14:6 (ESV)

It could also be a shortened version of "the way to salvation" (Acts 16:17).

"The Way" was considered a sect (Acts 24:2-5) in those days by the Jews and therefore they bounded and imprisoned both men and women (Acts 22:4-5) and in some cases they were executed (Acts 7:57-59, 8:1). Paul, one of the persecutors, testify this about his former life before his conversion:

For you have heard of my former life in Judaism, how I persecuted the church of God violently and tried to destroy it. -- Galatians 1:13 (ESV)

Ironically, he failed to destroy the "church", but rather advanced it to other regions in the Roman empire:

Now those who were scattered because of the persecution that arose over Stephen traveled as far as Phoenicia and Cyprus and Antioch, speaking the word to no one except Jews. But there were some of them, men of Cyprus and Cyrene, who on coming to Antioch spoke to the Hellenists also, preaching the Lord Jesus. -- Acts 11:19-20 (ESV)

Therefore, the Roman government also got involved with the persecution:

About that time Herod the king laid violent hands on some who belonged to the church. He killed James the brother of John with the sword, and when he saw that it pleased the Jews, he proceeded to arrest Peter also. -- Acts 12:1-3 (ESV)

These persecutions would have made it impossible to institute public church services in church buildings like the modern Christians are used. Instead, the believers gathered informally in private homes (Acts 12:12), most likely in secret.