How does the atomic number of an element identify it?

If #Z=1#, the element is hydrogen; if #Z=2#, the element is helium; If #Z=3#, the element is lithium;.........if If #Z=26#, the element is iron; etc.

Because most matter is neutral, if there are 26 protons within the nucleus, there MUST be 26 electrons, fundamental negatively charged particles of negligible mass associated with the NEUTRAL element. Note that the nucleus can contain different numbers of neutrons, fundamental massive nuclear particles with neutral charge, which act to bind the nucleus together. The presence of neutrons gives rise to the existence of isotopes: atoms of the same element with different atomic masses.

For hydrogen, #Z=1#, and again since #Z=1#, this is what identifies the atom as hydrogen. Most hydrogen nuclei contain only the 1 proton, the #""^1H# or protium isotope. A small percentage of hydrogen atoms contain a neutron, and this we would represent as #""^2H#, the deuterium isotope. A smaller percentage of hydrogen atoms contain 2 neutrons, to give #""^3H#, the tritium isotope. I stress that protium, deuterium, and tritium are ALL isotopes of hydrogen because #Z=1#; the presence of different numbers of neutrons in the nucleus gives rise to the isotopic distribution. Capisce?