What is or are the mechanism(s) behind the naming conventions for a church building or organization?

Orthodox churches (and monasteries) are most typically named after saints, in which case the saint in the name is the patron saint, although an Orthodox church might instead be named after a certain icon, a certain feast-day, or a certain title or aspect of God. Each church contains at least one relic of a saint. For example, my church is named after St. Nicholas of Myra, and a small square of one of his vestments in encased with his icon in the church. (Also, a relic of a martyr is placed in a certain spot inside the altar during its consecration, since Christian altars were first sarcophagi in the Roman catacombs, relics are holy, as in 2 Kings 13:21, and the altar is an image of the altar in heaven in Revelation 6:9, under which there are or will be souls of marytrs.) When a church is consecrated, a certain service is required.

More examples of names:

• Hagia Sophia (Holy Wisdom, an aspect of Christ)
• Church of the Resurrection (a.k.a. Holy Sepulchre)
• Saint Catherine's Monastery at Mount Sinai
• Dormition of the Mother of God Orthodox Monastery
• Holy Trinity Cathedral of San Francisco
• Kursk Root Icon Russian Orthodox Church

Catholic Parishes are faith communities named after a Catholic Saint; a combination of Saijts whose names appear together in the Liturgy of the Mass; a title of Our Lady; or a title of the Holy Trinity.

Examples:

• St. Augustine Parish
• Sts. Pepetua and Felicity Parish
• Holy Mother of Consolation Parish
• Divine Mercy Parish

Within Baptist churches, there tends to be a significant number of ordinal and locational church names, although the modern trend is to eschew both "Baptist" and incorporate more soteriological concepts. So, let me unpack that:

1. Ordinal naming

   Baptists are a highly missiological group - they want to plant as many churches as they can, and are often highly aware of their parentage. When a new Baptist church is planted in a particular area, it is often named for the area. The First Baptist Church of {Clarendon | Crewe | Alexandria | insert all sorts of cities where I've attended} is often succeeded by the Second Baptist Church of {X}. (And, incidentally, African American Churches tend to be 'Second Baptist of X' a lot, because the whites kicked out the blacks at a certain point.)

2. Locational naming

   Absent a First or second, there is often just a {X} Baptist church, when it isn't expected there will be more than one. I have preached at Middleburg, Marshall, The Plains, and Antioch Baptist churches, for example - all based on the place name. Because the city or place is sufficiently ambiguous, some churches in cities will just take the name of the street. In Washington DC, Sixteenth Street Baptist has historically been known as that - although it is now going to a First Baptist of DC moniker in order to establish its history. Martin Luther King, Jr. served at Dexter Avenue Baptist Church, which incidentally is located on Dexter Avenue, right below the State Capitol. (Got to visit that church and had a 'D'oh' moment on that one.)

3. Soteriological Concepts

   The more more modern church naming scheme tends towards concepts. "United Baptist Church" in Annandale was the merger of two locationally named churches (Barcroft and Annandale). Fireside Church, New Life Church, and many other 'Community Churches' (eschewing the name 'Baptist') now pop up. These tend to be younger and 'edgier' than the old First and Seconds.

What is rare amongst Baptist is naming after a Saint. Baptists as a whole tend to be rather leery of anything "Popish" and because of their love of local autonomy, tend to avoid tying themselves to any one individual. While there is the occasional William Broaddus Memorial Church or Smith Memorial, it is very rare to find a "St X of X" Baptist church.