Do you think “Alexa” and “Siri” were in response to millions of people already begging to say these names ? The brand recognition came from the names being used.
A name/word that will not be used in ordinary conversation is desirable. While talking to “computer” is popular (especially for Trekers), “Computer” or “House” would create too many false positives in many homes (especially while TV/radio news is in the background). In fact existing brand recognition would be a problem as it increases the chance of false positives.
I do agree with Hedda that Assist should provide a choice of several well-developed wake words, though I suggest a bit more discussion on which phrases would be best.