Rudimentary atomic theory was independently “discovered” multiple times and places throughout history.

Hippocrates also described the four humors.

Their theory of atoms was also that they were indivisible, being the most basic building block of all matter. Obviously now we know that that's not true.

They described a lot of things, and were wrong more often than not. Their biggest contribution was really just progress in the scientific method itself.

Basically, Empedocles came up with the 4 'roots' of air (smoke), water, earth and fire, Plato expanded on how they 'worked' and interacted, as well as naming them 'elements', and Aristotle expanded further on this and added the concept of aether, which is what stuff in the heavens must be made of.

Probably the most popularly read material on this both in ancient times and today is Aristotle and Plato. Plato also associated the first four elements with Platonic solids.

Atomic theory of today is really only named such because Atom is roughly the Greek word for 'indivisible'. Their indivisible atoms were of the four or five elements as they had no understanding of Chemistry.

Chemistry also linguistically does come from Alchemy, which comes from Al Khemia, which roughly in context means the study of the wisdom of Egypt.

This is because basically after Rome broke apart, many of the remaining scholarly texts of all kinds of philosophers largely only remained intact in Egypt.

So you had the Greek or Coptic texts translated into Arabic, studied and preserved in Arab speaking areas, which were then reacquired by various Europeans and translated into Latin or other local language. Roughly, the texts of this period which attempted to further philosophize more detailed understanding of elements, mixed with a huge amount of religious and superstitious content, became Alchemy.

When modern science began roughly with the Renaissance, well a lot of those guys were studied in Alchemy and attempting to apply more rigorous and testable logic to it, and we end up with the word Chemistry.

Thats a really long way to say that basically Atom as a word in modern parlance basically is just Greek for something that cannot be further divided, and is named such to basically honor the tradition of it all getting kicked off by the ancient Greeks.

Actual ancient Greek Elemental theory has basically nothing in common with modern Chemistry, and of course we now know that Atoms are actually divisible into Protons Neutrons and Electrons, and Protons and Neutrons are further divisible into various Quarks.