Most states have municipal well filling and sealing ordinances to ensure the unused well doesn't cause a problem to the property owner or to the environment.

I knew someone who was having their basement concrete floor jackhammered out when suddenly the operator lost control of the hammer when it broke through and ended sliding into the well. I don't recall how they filled the well.

WOW!!! Good question! I looked up "cistern" on wikepedia and it looks just like that!
It is about 15" in diameter and is 17 feet deep. It is completely hand-dug, with rocks lining the main part of it and then a cement ring around the top.
The only reason we thought it was a well is because it has pipes that run out of it and go out into the ground.

Cisterns have to have overflows, so the pipes may be that......or it may have been to a hand pump or even electrical pump. We had a shallow well electrical pump to our spring cachement (cistern) until we built a large reservoir to catch it as it overflowed from the cistern and we now have pipes from the cistern to an old fashioned pitcher pump in my kitchen, like was here before it got modernated. LOL. So, I have inside water even when our electric goes out and I use it daily.

If you could, and have time, pump it out and see what might have been dropped to the bottom.

I know that a lot of neat, and some very valuable, things have been found in old wells over the years.

As for what to do with it, since it's small, and if the cement ring is in good shape, I'd say simply drop a cement slab over it to seal it, but make sure you provide provisions for overflow under the floor just in case the well decides to breach for some reason.

I grew up in a house built in 1701 in Boston. We found an old well under slabs of cement in the first floor of the barn.

The well was full to the top with old china, medicine bottle, tools, shoes - you name it - all from the 1800s. Not every item was still intact - some of the china was broken.

It was fascinating!

The down-side was that I was a little girl at the time and my parents didn't really know what to do with our discovery. Most of the items were tossed out and some was left behind for new homeowners when we eventually moved away years later.

If only I could go back in time and save those items...UGH! What a shame!

I found a lot of 19th Century glass bottles at one end of an excavation I did in 1996. Then it occurred to me they were probably from an old privy, which reduced their attractiveness to nil.

Seems like a shame to fill it in.

Safely sealing it with a concrete tile, with some provision for overflow, seems like the best way of gently decommissioning yet preserving it.

Who knows, in 50 years people may be retrofitting those old cisterns as mini geothermal heating systems.