I have noticed that such churches only contain geographical references (like "Smallville Church of Christ" or "Gotham Heights Church of Christ"). Why don't they use verbage like "First", "Calvary", "Trinity", "Faith", or "Grace" in their names?
No authority in scripture to use such terms.
There is authority to use church of Christ and just add the city name to it, example verses being:
Romans 16:16 - churches of Christ are mentioned not trinity church or first baptist church
Revelations 2 and following - every church being written to is being mentioned by city name
1 Corinthians 16:1 and 19 - churches mentioned by city name, however, they are still churches of Christ. To be more specific WHICH church of Christ, you would mention where they are, hence example "first street church of Christ" or "Galatian church of Christ"
Matthew 16:18-19/ Acts 2 - It is Christs church and therefore He has ownership of it. Which gives authority to call it church of Christ and not Grace church or Methodist church.
In any case, “The church of Christ” is not a denominational title that describes a religious institution established by men. Rather, it is the collective reference to the people of God in the world, people who follow the New Testament teaching regarding the church.