The early Christians were a Jewish sect in Jerusalem and they became known as Nazarenes. They possibly took this name as Jesus was sometimes known as the "Nazarene." Another reference I've found states that the term comes from the Hebrew word "Netzer" as found in Isaiahh 11:1, and means a "branch," thus they could have been called the Branchites, or followers of the one they considered to be "The Branch." The word Nazur in Aramaic means separate, so they could also have gotten their name from being a new, separate sect of Judaism, and may have been a derogatory term, that they accepted for themselves.
One of the greatest of miracles is how Christianity spread from the 120 or so followers in the beginning of Acts to the largest world religion. They also referred to themselves as "The Way" (Acts 24).
The term Christian actually developed later by the Greek followers as they attempted to translate the term "Nazarene" and it means "Messianists". This would have possibly been a derogatory term as well, that the early Christians made their own.
The Nazarenes were located in Jerusalem and lead by several of the Apostles who had known Christ, such as Peter, and were led by James the Just whom some believe was the brother of Jesus, or perhaps a cousin.
The Nazarenes lived a Communal life, dedicated to spreading the Good News, and accepting Gentiles into the fold.
Another group of Christians in Jersusalem were the Ebionites. They followed the Jewish traditions and Mosaic Law, as well as the teachings of Christ, but did not consider Christ divine, and followed the Nazarene Church of Jerusalem and rejected Paul's spreading of Christianity to the Gentiles, without the Gentiles becoming fully Jewish in practices.
The early Christians believed that the leader of the Church was the community of the Nazarenes in Jerusalem. This changed when the Romans decided they had enough of Hebrew Revolution and Zealotry and in 70 AD they entered the city in force and killed those that refused to leave the city. Peter had moved to Rome, and it would eventually be the seat of the Church on Earth.
So by 70 AD there were several Christian groups that had developed throughout the Roman Empire. Pauline Christianity, Nazarenes, and Ebionites.
Pauline Christianity would be the most successful. Though many other psuedo groups would develop over the next three hundred years, many of which would be considered heresies.