It’s strange that as of iOS 14.3 it isn't possible to activate Siri with device-specific names.
It’s "Hey Siri" or nothing.
This leads to some pretty frustrating experiences when you have more than one device that supports the setting “Listen for 'Hey Siri’.”
A quick example of one that happened to me earlier today: I'm sitting on my couch using my iPhone and decide to start playing some music in the background. I say, "Hey Siri, play playlist, piano chill."
Rather than playing from my HomePod as intended, it starts playing from my AirPods Max that happened to be resting atop my head (not over my ears).
While I know Apple tries to figure out what device you're most likely to be speaking to, in tricky situations like these (when you happen to be using one of your supported devices that you don't want to activate) — it fails almost every time.
We all agree that given available tech it’s too much to expect Apple to identify the intended device 100% of the time. Instead, they should add an option to select a unique wake word for supported devices. Simply being able to say, "Hey HomePod," or "Hey iPhone" would be a huge win.
Until then, I've resorted to disabling the "Listen for 'Hey Siri'" setting on all devices except for my HomePods. And, assuming I remember, temporarily enabling it on my iPhone for situations when it’s especially useful (like during long bike rides 🚴♂️)