Name for HxOy compounds?
Not only I've never heard of a name for such a class, but the very choice of compounds seems quite artificial to me. What feature do they have in common? 


Consisting of H and O? That would exclude oxygen and ozone.
Consisting of H and/or O? That would include $\mathrm H_2$ as
well.
Containing "active oxygen", whatever that might mean? That
would exclude water, but include a bunch of inorganic and organic
peroxides.
Oxide is indeed too generic; also, it does not include oxygen and ozone. Oxygenate is even farther off.


Why would you want to have such a class, really?