The names of elements are determined from their position on the Periodic Table. In the modern Periodic Table, the elements are listed in order by increasing atomic number.
The atomic number is the number of protons in the nucleus of an atom of a particular element. By knowing the number of protons, you know the atomic number. If you know the atomic number you know which element it is in the Periodic Chart. A good Periodic chart should give you enough information to determine the name of the element.
The atomic number is not only equal to the number of protons in a nucleus of an element, it is also equal to the number of electrons because atoms are neutral: protons = electrons.
The neutrons are not directly related to the position of an element in the periodic chart, however the number of neutrons can be determined by subtracting the atomic number from the mass number.