The symbols for atoms are those found on the periodic table, such as H for hydrogen and He for helium. These symbols are assumed to represent the atom in its "ground state"—that is, the condition where it has an equal number of protons and electrons, and therefore a neutral charge. Therefore we can say that the symbol itself, by default, represents the atom in a neutral state.
Ions, on the other hand, are by definition incapable of being neutral. An ion is an atom in a state where it has more or less than the ground state number of electrons. For example, an oxygen atom would normally have 8 protons and 8 electrons in its ground state, for a combined charge of 0. If the oxygen gained one extra electron, it would have a total charge of -1, and it would be considered an ion. If the oxygen lost an electron, it would have a charge of +1, and this would also be considered an ion. However, in neither state does the atom have any kind of overall neutral charge, so it cannot be represented that way. The representation for an ion is to show the symbol for the atom, with its overall charge in a superscript on the top right corner.