What is an atom called when it has no charge?
An atom has no charge. The number (and charge) of protons in atom's nucleus is balanced by the electrons orbiting the nucleus.
If it had charge it would be called an ion. In an ion there is no balance between the number of protons and electrons.
If there are more electrons than protons then it is called an anion.
If there are more protons then it is called a cation.