From what I understand atomism subscribes that an individual atom is the "indivisible" fundamental component of all physical things. Ever since the atom was split, and even more "base" non-atomic objects such as quarks were discovered, does this invalidate the theory?
The ancient atomists just used "atoms" as a word for the smallest unit of matter, they didn't associate them with modern elements like hydrogen, carbon, oxygen etc. because this notion of all forms of matter are either mixtures or pure distributions of these basic elements didn't come until the discoveries of Lavoisier in the 1700s leading to the discovery of the periodic table by Mendeleev in 1869. In between those, the work of John Dalton made the case that the specific ratios of different substances needed to make some other substance with none left over (the ratio of hydrogen and oxygen needed to make water with no oxygen or hydrogen left over, for example) could be explained if each element were composed of tiny units, which he called "atoms".
But since the ancient Greek philosophers weren't thinking in terms of the modern notion of elements like hydrogen and oxygen, if they could learn of subsequent science they'd have no reason to be bothered by the later discover that Dalton's atoms were actually made of smaller units, they could simply say that Dalton was mistaken in identifying the units he discovered with the older philosophical notion of "atoms" and that whatever turn out to be the most basic and indivisible units (like quarks and electrons and other fundamental particles) are the real atoms.