How do mobile companies change the boot animation?
They don't have to change the ROM on every phone by hand. They have a relationship with the phone's manufacturer, so the carrier's customized ROM gets installed on the phones at the factory. This customized ROM might include their boot animation, bloatware, settings (e.g. APNs) for their network. These phones often also have slightly modified hardware: the outer shell badged with the carrier's logo, or in a different "exclusive" colour.