Rename Siri on HomePod ?

You can potentially set things up such that the HomePod can respond to Hey Siri or Siri while the iPhone only responds to Hey Siri and then use the shorter Siri trigger phrase which only the HomePod should react to.

tt2

You can't change the name you call Siri.

I have observed that, in a room with a Homepod, an iPhone and an Apple Watch, if I call for Siri, it's always the Homepod that answers. In this situation, the iPhone is usually locked. Additionally, if I'm in a room with my iPhone and wearing my Apple Watch, it's the Watch that responds if the iPhone is locked.

Placing the phone face down on a table works for me.