The subatomic particle that determines the name of an atom is the proton.

Here's why:

* Atomic Number: The number of protons in an atom's nucleus defines its atomic number. This number is unique to each element.

* Element Identity: The atomic number is what determines the element. For example, all atoms with one proton are hydrogen, all atoms with six protons are carbon, and so on.

While the number of neutrons (which can vary within an element, creating isotopes) and electrons (which can be gained or lost to form ions) can change, the number of protons remains constant for a given element, and therefore determines its identity and name.