What is the analogue of "molecule" for ionic compounds? In a system, if we have $\pu{18 g}$ of $\ce{H2O}$ ($M_\mathrm r = 18$), we can say we have a mole of water molecules or $6 \times 10^{23}$ molecules. But in another system, if we have $\pu{342 g}$ of $\ce{Al2(SO4)3}$ ($M_\mathrm r = 342$), what is the best way to say that there is one mole of "aluminum sulfates" or $6 \times 10^{23}$ "aluminum sulfates"?

Since it is a ionic compound, we can't say molecules, but I can't find an analogous form for ionic compounds. I thought about saying "a mole of aluminum sulfate ionic aggregates", but it still doesn't too good, since I've never seen a definition of ionic aggregate as a unit of the ionic compound formula. It only tells the way the ions organize themselves: as an aggregate.

I know it is a silly question, but in terms of language and symbolism, it is important to me as a chemistry teacher.
The term you are looking for is formula unit, I think. Wikipedia doesn't really describe it super well, but just to give an example, you could write the sentence


  $\pu{58.44 g}$ of $\ce{NaCl}$ contains $6.022 \times 10^{23}$ formula units of sodium chloride


and it would be pretty well understood.

See also: What is the difference between a Chemical Formula and Formula Unit?