While I understand the problem, I don't think that would be an elegant solution because we'd then have to remember multiple phrases.
A better solution would be for devices to understand which one you're trying to address and seamlessly transfer the request to the correct device. For example, it should never happen for the HomePod to tell you that it can't make a phone call, it should just redirect the request to the iPhone if it's nearby.
I see no reason why we shouldn‘t or couldn‘t fundamentally have both.
Have something like „Hey Siri-iPhone“, „Hey Siri-Mac“ and so on be a command that enforces Siri to listen from a device of our choice. Or more elegantly, allow us to tell Siri what device we want a command executed, i.e. „Hey Siri, search the web for XX
on my iPad“ would automatically have that command be executed on that device. Mind you, this is already possible for music playback thanks to AirPlay 2, so there‘s no reason why we shouldn‘t be able to direct any command to any compatible device at will.
Meanwhile device-specific requests are handled and transferred to the correct device automatically. For example „Hey Siri, call x“ Gould automatically transfer the command to the iPhone like you said, „open the documents folder“, „show all documents last edited on the 1st of June“ or any other Mac-specific command would always transfer to the Mac, have music-specific commands always be executed on the HomePod if in reach, and so on. Nevertheless, there will always be commands that can be executed on multiple devices, so having the ability to enforce which device receives a command on-the-fly would be necessary.
The current situation is just messy and un-Apple-like. I don‘t need my HomePods reminding me that they cannot search the web or define a word or open a folder or make a Spotlight search or show photos from a specific date. At first I was excited about the Hey Siri-catchphrase coming to the Mac, but now that I‘ve ordered a new MBP, I realized that when I‘m at home, I‘m mostly gonna use it in the same room my HomePods are in, and I don‘t want to turn off their Hey Siri-trigger either as I often control them with voice. So I‘ll probably end up not really using Hey Siri on the MacBook Pro.