A good response from Jeff Smith to that common question:
“What’s the name of your church?”
It’s a common enough question, but the answer is not necessarily so simple. First, if you have your own church, you are in direct competition with Jesus Christ, who also has his own church. We use that terminology very loosely to describe the church where we work or labor, but perhaps emphasizing Christ’s ownership would lead everyone to greater respect for his authority over the church.
Second, throughout the first century of the ministry of Jesus and the early existence of the church he built, it had no recognizable proper name. The apostles lived in a time during which no denominations existed, no pope had yet been imagined or ordained, and the need for identifying nomenclature was absent. The New Testament describes churches without any sectarian signification. There were no Baptist or Methodist Churches, no St. Paul’s or St. Bartholomew’s. Even when the congregations were described as “churches of Christ” or “churches of God,” there was no denominational intent, but only an acknowledgement of divine possession. The churches in Revelation were identified only by location. Their namelessness was a short-lived triumph over the divisive impulses of men.