If we add one electron to an atom, the atomic number remains the same because the atomic number is defined as the number of protons in the nucleus of an atom. The addition of an electron does not affect the number of protons in the nucleus.
However, the addition of an electron does increase the mass of the atom slightly. The mass of an atom is determined by the sum of the masses of its protons, neutrons, and electrons. Electrons have a much smaller mass compared to protons and neutrons, so the addition of one electron has a negligible effect on the overall mass of the atom.
In some cases, if the atom gains or loses electrons and becomes charged, it becomes an ion. In that case, the number of electrons will no longer be equal to the number of protons, and the resulting ion will have a different atomic number and overall charge. But if we are specifically considering the addition of one electron to a neutral atom, the atomic number remains the same, and there is only a minimal change in mass.