How did atom obtain its name?

The word is derived from the Greek word "atomos", meaning indivisible. The concept of the atom originated round 440 BC. In Greek, the prefix "a" means "not" and the word "tomos" means cut. Word "atom" therefore comes from "atomos", a Greek word meaning uncuttable. 

In 1803, John Dalton formulated the "atomic theory" of matter based on experiments that quantified the weights of elements formed when compounds were broken down. Based on experimental evidence, Dalton proposed that atoms really do exist as fundamental units of all elements. 

Twentieth century physics was able to probe atoms and prove that they are not, in fact, indivisible. But the name stuck, and still has meaning in that atoms are the smallest, indivisible part of any element. If you do divide them into smaller pieces of protons, neutrons and electrons, you no longer have the original element.

What is Dry Ice?

Dry ice is nothing but solidified Carbon Dioxide (CO₂). When Carbondioxide is cooled to a very low temperature it transforms into solid. The  temperature is about -78 deg centigrade. 

Carbon Dioxide is an interesting material because, at normal atmospheric pressures, it has no liquid state. It can only obtain a liquid state under very high pressure in a containment vessel.

So, when you have a frozen chunk of carbon dioxide out in the open where you can see it, it will transform directly from its solid state to a gas state with no intermediate liquid state. This process is known as 'sublimation'.

Dry ice freeze water vapor in the air near it producing visible vapor all by itself, however adding water will also add substantial heat which will cause the solid CO₂ to sublimate at a greatly accelerated rate thus producing much more visible vapor.