Short answer: you can't.
However, you don't necessarily need to do so for some things. For example, if you're asking for their name - it probably won't change, so you can ask for this the first time and then cache the answer.
If you're using the node.js library, you can easily do this by adding the information to the app.userStorage object. This will be saved for you in between sessions. So your code might look something like this:
var userName = app.userStorage.userName;
if( !userName ){
if( app.isPermissionGranted() ){
userName = app.userStorage.userName = app.getUser().displayName;
} else {
requestPermission();
}
}
(Tho I haven't tested this, it looks roughly correct.)
If you're requesting location, this may or may not be as good a solution. Although a Google Home device has a fixed location, using the Assistant from the phone can change. In this case, you'll need to re-request it each time.
Clearly this isn't desirable in a lot of situations, and the team is aware how poor an experience this is. No promises on when, but hopefully they're working on a better solution.