How to have Siri recognize my new voice?

If Siri doesn't recognize you:

Siri might ask you who you are from time to time. You can respond with your name, or you can even begin a request by getting Siri's attention and saying "This is [your name]" or "Who am I?" If Siri calls you the wrong name, say "No, this is [your name]." Siri calls you by the name that you have set in your My Card. If you have the same name as someone else sharing your HomePod, you can change the name in your My Card to a nickname.

And See Tell Siri how to say your name.

Set up voice recognition on HomePod or HomePod mini - Apple Support

Ok you said new voice. It’s the mic not hearing you. Try a slight rotation of the HomePod so the mic’s inside are aimed towards your voice. Make sure nothing is blocking the HomePod.