I've tried to find an answer to this, but I cannot find anything historical (most responses are along the lines of "to honor or invoke a patron saint"). In the New Testament, the different congregations are just called by their location and I assume they rarely if ever had specific church buildings in those early years. Do we know when and why Christian's started naming churches after specific individuals/saints?
The earliest dedicated sites and monuments are those of martyrs. Christians built shrines and small buildings in their memory, a practice long-established in the pagan veneration of mythical heroes, kings, and chiefs. The earliest surviving example is underneath St. Peter's in Rome, dating to late second century.
See Krautheimer and Curcic, Early Christian and Byzantine Architecture.