If you prefer to access it via your iPhone's control center, you can configure it that way in the control center settings. It is called "Music Recognition" there.

Nice I will have to check this out, control center is definitely a great little overlay but I haven't reliably figured out how to add things to it. I will investigate further.

For general information have a look here [0]. Also be aware that elements in the control center might even offer additional functionality, e.g. like setting the brightness of the flashlight. In this case instead of just switching the flashlight on by a tap on the button, keep the flashlight button pressed to bring up a slider to set the brightness. Just play around with the other control center elements to find out what is possible.

[0] https://support.apple.com/guide/iphone/iph59095ec58/ios

I usually say "Hey Siri, what song am I listening to?" but it works with a bunch of variations e.g.: "what song is this?"

There's also a bunch of other options to trigger Shazam, main way I use it is from the Control Center: https://support.apple.com/en-us/HT210331

If you have an Apple Watch, you can also set it as a home screen button, which is a lot more discreet in public.

I just say Hey Siri Shazam this.

“Hey Siri, what song is this” works