An atom's identity is primarily determined by the number of protons in its nucleus, which is referred to as its atomic number. Each element on the periodic table is defined by a unique atomic number, which corresponds to the number of protons present in its atoms. For example, hydrogen has an atomic number of 1 (one proton), while carbon has an atomic number of 6 (six protons).
In addition to protons, the number of neutrons can also play a role in defining isotopes of an element, which are variants of the same element with differing numbers of neutrons. However, it is the number of protons that fundamentally determines the element itself.
Electrons, which are negatively charged particles that orbit the nucleus, do not determine the identity of the atom, but they do influence its chemical behavior and properties. The arrangement and number of electrons define how an atom interacts with other atoms, leading to the formation of chemical bonds.