Hi guys, not sure if you're still having this issue but I created an account on this site just to respond to this Thread. I've just purchased a HomePod and was struggling with this exact same thing for two hours, almost throwing the HomePod out of the window, untill I read @CamiMR's last comment that pushed me in the right direction, thanks a lot!
So I immediately saw what the problem was when I did this:
Settings -> 'click on your name' -> iCloud -> Scroll down to Siri
Turns out Siri never sent my trained voice to iCloud! So the HomePod obviously couldn't pick it up. I turned it on and it works flawlessly now. I hope this helps you set it up for you, it did for me at least.
Only saw your post today, and FINALLY got it sorted!!
Siri was turned off in her iCloud settings (never thought of checking this), and as soon as I turned it on it started recognising her voice immediately!!
Thank you so much @JochemvdMeer