I don't think there's an alternative name for them. An individual one is named by putting the metal first, then the non-metal with its ending changed to -ide.
Examples: sodium and chlorine make sodium chloride.
Magnesium and nitrogen make magnesium nitride.
The ionic compound CuCO is called copper(I) carbonate.
The ionic compound Ca3As2 is called calcium arsenide.
The ionic compound CuF2 is called copper(II) fluoride.
The ionic compound CoCl2 is called cobalt(II) chloride.
The ionic compound Pb3N2 is called lead (II) nitride.
The ionic compound CuCO is called copper(I) carbonate.
The ionic compound Ca3As2 is called calcium arsenide.
This is an ionic compound, for example a salt as potassium chloride.
This is called ionic bond.
The ionic compound CuF2 is called copper(II) fluoride.
The ionic compound CoCl2 is called cobalt(II) chloride.
The ionic compound Pb3N2 is called lead (II) nitride.
The ionic compound AlN is called aluminum nitride.
SO3 is a covalent compound, not ionic. It is called sulfur trioxide.
The ionic compound Mg3P2 is called magnesium phosphide.
Silver bromide.
The ionic compound BaSe is called barium selenide.