What is the chemical name for the ionic compound $\mathrm{C}{\mathrm{a}}_3{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ ?

Positively charged cations and negatively charged anions combine to generate neutral ionic compounds (most commonly).
Typically, non-metals gain electrons to have a net negative charge, creating anions, while metals typically lose electrons and hence have a net positive charge to become cations.
Strong and brittle, ionic compounds have high melting and boiling points.
Knowing the cation, its symbol, and its charge as well as the anion, its symbol, and its charge is the first step in writing an ionic compound. In ionic compounds, the positive charge, or cation, is written first, followed by the negative charge, or anion, to create the neutral molecules.

Ionic compounds do not exist as molecules. They are solid crystals like sodium sulfide. The compound $\mathrm{C}{\mathrm{a}}_3{\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ we gave is calcium phosphate, which is made up of cationic calcium and anionic phosphate. 

The cation calcium is ${\mathrm{Ca}}^{2+}$ and the anion is phosphate $\mathrm{P}{{\mathrm{O}}_3}^{4-}$. This formula shows that every two phosphate groups contain three calcium ions.

Hence, option A is correct.