The only stable, and only naturally-occurring isotope of gold has mass number of 197. This is the number of protons and neutrons in each nucleus.
Gold's atomic number is 79. This is the number of protons found in each gold atom. This determines its place in the periodic table, and its chemical properties: it is the defining property of gold.
A nucleus with a different number of neutrons and the same 79 protons would be a different isotope with a different mass number; a nucleus with a different number of protons would not be gold, but some other element.