Question

What does it mean to say that the protons give the atom is identity

Answer 1

The number of protons tells you what element an atom is. Just knowing the number of neutrons/mass number does not tell you what element an atom is, since atoms of the same element can have different mass numbers. But all atoms with the same number of protons, are also always of the same element.

Hence, we can identify an atom by the number of protons it has