How do I tell Diablo 3 I no longer want a key binding?

You can unbind a key by binding it to a different action, and then changing the key for that other action a second time.

Taking your case as an example, we want V to be unbound.

We'll start by opening up the keyboard settings and binding "Toggle Inventory Menu" to V instead of the default I.

You'll see a message at the bottom of the keybindings window stating that "Show Player Health Bars is Now Unbound!"

Now that "Show Player Health Bars" is no longer bound to V, change "Toggle Inventory Menu" back to using I.

Now V is no longer bound to any Diablo 3 function, and is free to use as your push-to-talk key.

These steps are also useful if you find yourself accidentally pressing keys like "show/hide party" and wondering why you can't see anyone on the minimap, and want to make sure you can't accidentally turn it off in the future.

One way to do this is by hovering your mouse over the bind you wish to remove, then pressing the Del key.