It's also something of a persistent anachronism that lends itself to the historic population centers, I suspect. The actual test location was at Trinity Site, which is closer to present day Socorro and Carrizozo[1] than to Alamogordo and detonated on the north end of what was then called the "Alamogordo Bombing Range." This location is now a part of the broader White Sands Missile Range. It gives me some amusement as a local, because we occasionally hear the question "Oh, Alamogordo? That's where they tested the bomb, isn't it?!"
I hate to disappoint their curiosity, of course, but according to present day geography, no; historically—kind of—if you consider everything was then associated with Alamogordo, including the army air base! To us, Trinity Site is 80 miles to the north/northwest and on the other side of the Oscura Mountains (north of the San Andres Mountains)!
[1] https://www.google.com/maps/@33.6815401,-106.4737885,20277m/...