Without getting too much into philosophy, what do you mean by the identity of a substance and "what a substance definitively
is." In naming a substance, atomic number plays a crucial role. In this case, you can say that scientists somewhat artificially link the number of protons in an atom to its identity.
However, if you consider the chemical and physical properties of the element as an essential part of its identity, then the valence electrons are more important in determining an element's identity than the number of protons. Sodium is reactive because it has 11 electrons, not because it has 11 protons.
Here's a bit of an extreme example. In a paper published this week in the journal
Science, researchers made helium act like hydrogen by replacing one of the electrons in helium with a negative muon. Because the negative muon is 207 times more massive than the electron, the muon "orbits" much closer to the nucleus and cancels out one of the positive charges so that the electron "feels" only the pull equivalent to one proton. Even though this species has two protons, it can substitute for hydrogen in chemical reactions.
Similarly, the researchers can create a hydrogen-like species with no protons by creating a species where an electron orbits a positive muon. This hydrogen-like species can also substitute for hydrogen in chemical reactions.
Here's the citation for this paper:
Fleming et al.
(2011) Kinetic Isotope Effects for the Reactions of Muonic Helium and Muonium with H2.
Science 331: 448. http://dx.doi.org/10.1126/science.1199421" (subscription required to read the paper).
A summary of the study is available here:
http://www.newscientist.com/article/dn20049-atomic-disguise-makes-helium-look-like-hydrogen.html