It looks like the fitting is designed to accept some kind of rubber/plastic hose and it held in place with a clamp. An ordinary hose clamp would work but there was probably something more decorative at one point in time.

I'd suspect that the fitting could be removed, although it might not be easy. Then replace it with a conventional threaded adapter and you could use something like this:

The unfortunate part is that handheld showers tend to be a lot more expensive than a conventional one. Depending on how skilled you are and how concerned you are with appearance you could probably rig up something that uses a a conventional shower head for a whole lot less money.

It's a clawfoot bathtub faucet.