Google Assistant on phones is getting the Hey Google command pushed out to it, a hotword which had previously only been available on Google Home devices. The rollout is starting on some phones but has not reached all users yet, so it's entirely likely that it could take at least a few more days before most users with Google Assistant access on the phones will see this pop up. The good news is that you should immediately notice it, as there will be notification that surfaces in the notification shade which tells you to retrain your Assistant with the new hotword, which as you may have guessed will let you activate Google Assistant with either this new command, or the usual OK Google command.
You'll need to be on the latest version of the Google app for this prompt to appear, so if you're not then that may be one reason why it hasn't shown up, that is assuming that it hasn't actually shown up for you. Of course, it is possible that someone could simply dismiss the notification before reading it, not knowing what it is. In which case you should be able to go into the Google app, navigate to settings, find the hotword options and train Assistant for the new hotword from there. Otherwise you may jut need to wait for it to show up on its own.
For those that use Google Assistant often, this is a step in the right direction for customizing the interaction experience. It's still not the same as being able to set your very own hotword to whatever you want, but it is something, as it's better than only having one hotword to begin with. Whether or not Google ever makes it possible to set up your command to be whatever you wish is still a mystery. For now, though, there's at least one more option now for users who access Google Assistant mostly on phones. Another benefit is that Hey Google may be simpler to say for some users, which means there might be a higher chance of the phone recognizing the command without any issues.