Cortana can be trained to only respond to a specific user's voice by having the user say six sentences out loud to Cortana in a quiet place, which allows Cortana to learn and recognize that individual's voice so that only they can activate Cortana with voice commands and not others passing by.

1. You can train Cortana to only respond to your voice,
that way not just anyone passing by can shout out Hey
Cortana in passing and accidentally her (or
maliciously) on. To do this you need to train Cortana to
listen to your voice. Make sure you are in a quiet place
before you start these steps.
How to train Cortana to respond to
your voice only on Windows 10

2.  Press the Windows key + S together to open
Cortana.
 Click the Notebook button. It's the little notebook
icon underneath the house icon on the left side of
your screen.
 Click on Settings.

3.  Click on Learn my voice.
 Click on Start.
 From here, Cortana will instruct you say six
sentences out loud, so make sure you say them
loudly and clearly. Once you're done, Cortana will
know your voice and respond only to your
commands.