Having a Smart Speaker at home that is limited to one family member was an issue identified and fixed first by Google in April 2017. Since October, last year, Amazon announced customized voice detection also on Alexa.
For Amazon, this was a catching-up game with Google, and since October the only features available were Flash Briefings, shopping, Amazon Music’s family plan and Alexa to Alexa calling, but now it is also available for developers / Alexa skills.
Alexa Voice Profiles, according to VentureBeat, is limited to 10 profiles.
Video about Alexa Voice Profiles
On HomePod of Apple, unique voice recognition should also be available as Apple owns a patent that allows Siri to know an individual voice.