Earlier quoted context omitted.
When you train your phone to understand "Hey Siri" it requires an internet connection for the training so that it can verify that you are actually saying, "Hey Siri" and not "Yo, phone spirit". After the initial training, it no longer requires (or uses) the internet to detect the keyphrase. You are asked to do a few iterations of training so that the phone has a model on your voiceprint for "Hey Siri". Which is why,…
This explanation does not explain why neither Google nor Apple allow you to change the wake word. Myself, I believe any technical reason, if it actually exists, is a secondary factor - the primary reason is branding. They don't want people changing wakewords, because as long as everyone uses the same, "Ok Google" and "Siri" are terms/brands.
I also believe it is restricted mainly for branding and easy marketing.