The identity of an element is determined by the number of protons in the nucleus of its atoms. This is known as the atomic number. Each element has a unique atomic number, which defines it and distinguishes it from other elements.
Neutrons contribute to the atomic mass and can affect the stability of an isotope, but they do not determine the identity of the element itself. Electrons are responsible for the chemical properties and behavior of an element, but they do not define which element it is.
Therefore, the subatomic particle that determines the element's identity is the proton.