What do we call this number which is characteristic of a particular element?

Hint: Elements are the simplest complete chemical substances and each element corresponds to a single entry on the modern periodic table. It is a material that consists of a single type of atom and each atom contains the same number of protons.

Complete answer:
The number which is characteristic of a particular element is called atomic number. The atomic number of an element is also called proton number. It is equal to the number of protons found in the nucleus of every atom of that particular element. It uniquely identifies a chemical element. The sum of the atomic number and the number of neutrons is equal to the mass number of an atom. Atoms which have the same atomic number but different number of neutrons and different mass numbers are called isotopes. The atomic number is denoted by the conventional symbol $Z$ which comes from the German word Atomzahl meaning atomic number. Each element has a specific set of chemical properties as a consequence of the number of electrons present in the neutral atom i.e. $Z$ . The configuration of these electrons follows the principle of quantum mechanics.
Therefore, the number which is characteristic of a particular element is called atomic number.

Note:
The number of electrons present in the electron shells of each element, mainly the outermost valence shell, is the primary factor in determining its chemical bonding behavior. So, it is the atomic number alone that determines the chemical properties of an element.