The way we were
To understand why you may encounter ATP synthase referred to as ATPase, you need to be aware of the historical context — the experimental work that preceded the knowledge of the structure and function of the enzyme complex that we have today. In a nutshell:
Original studies of the components of what we now know to be a complex capable of synthesizing ATP could only be assayed by their ability to hydrolyse ATP. Even though these components (F1 and F1FO) were derived from a mitochondrial system that coupled electron transport to ATP synthesis, and the authors believed these components were responsible for ATP synthesis, they were obliged to refer to them by the activity they had assayed: hence F1 ATPase and F1FO) ATPase.
It is instructive to consider a paper by Kagawa and Racker, published in 1966, and entitled:
Partial Resolution of the Enzymes Catalyzing Oxidative Phosphorylation
VIII. PROPERTIES OF A FACTOR CONFERRING OLIGOMYCIN SENSITIVITY ON MITOCHONDRIAL ADENOSINE TRIPHOSPHATASE”
This work demonstrated that a mitochondrial ‘fraction’ (FO — ‘F’ stood for ‘fraction’) when added to another ‘fraction’ (F1), previously shown to have ATPase activity, could confer sensitivity of the ATPase to inhibition by oligomycin, a compound that inhibits oxidative phosphorylation in intact mitochondria. The title shows clearly that they were aiming to understand ATP synthesis, but were at the stage where all they could measure was the ATPase activity of fractions. It was not until 1973 that Racker and Stoeckenius were first able to synthesize ATP, and for that they had to use a different system — the light-activated purple membrane of Halobacterium halobium. The key was the incorporation of the membrane — without it there could be no proton gradient to drive the synthesis of ATP, and this was why the isolated F1FO) complex could never catalyse synthesis of ATP on its own.
Those days are gone now
The structure of the components of the ATP synthase finally started emerging in the 1990s, after which no doubt remained that the F1 and FO fractions were part of a synthase.
Therefore, in describing the enzyme complex as we now know it to be,
there is no excuse to refer to it as anything other than ATP synthase. Moreover there is a particular need to avoid confusion with a membrane ATPase (below).
In my opinion, any textbook that refers to ATP synthase as ATPase is severely out of date and should be burned.
Of course, I exempt historical accounts, as long as the context is made clear.
The acid test
In some cells there are transmembrane complexes, structurally related to the mitochondrial (or bacterial membrane) ATP synthase, that are ATPases. These are the Vacuolar-type H+-ATPases (V-ATPase) which use the energy of ATP hydrolysis to transport hydrogen ions across the membranes of certain tissues and organelles. Another reason not to refer to the ATP synthase as ATPase!