When exposing entities to the google assistant using HA Cloud you can’t change the name in the UI of how they are exposed. You can with manual config: https://www.nabucasa.com/config/google_assistant/#manual-configuration
Don’t know if this is the same for Alexa. If so, would probably be nice to also see it added there.
Yes you could also do that from the Google Home app itself but sadly not for scripts. (Since google just removed the ability to see those as scenes in the app when they are not in rooms, so when you add a new one, good luck changing it’s name or adding it into a room & house.)