Unknown shower faucet part
That is the chrome inner sleeve from a knob that is now missing its external finned plastic portion.

If it is not pulling off easily (they pull directly off, just like a knob should...) then you may need to use a faucet handle puller to remove it.

Of course there are tricks-of-the-trade, like using penetrating oil and spraying up where the valve-stem splines meet the (probably corroded) sleeve spline and tapping (gently) around the outer part to get it to break away...