Trivial name of a compound vs its chemical formula
No you are absolutely right here, but even sulphate or nitrate is wrong. If you take a closer look at what a sulphate essentially is, you will see the following: It is a separate unit, it has a central atom and ligands and the whole unit is negatively charged. If this was a metal we would say it's a complex and name it with some sort of -ate in the name. And this is exactly what you see here. So tetraoxosulfate in short is sulfate. Whit this shorter notation you are just not able to guess it unless it is so common that you should know about it. For lithium aluminium hydride it's the same thing, it should be called lithium tetrahydroaluminate. 

Now you may ask yourself how are you supposed to work with these problems? In all scientific cases just google it. That's what we do as well, if this is class or homework related, then your teacher will only give you certain examples. If he doesn't, talk to him about it.