Pottermore speculates that the Chamber was initially conceived as a place where Salazar Slytherin could Secretly instruct his pupils in magical techniques the other Founders disapproved of:
Perhaps, when he first constructed the Chamber, Slytherin wanted no more than a place in which to instruct his students in spells of which the other three founders may have disapproved (disagreements sprung up early around the teaching of the Dark Arts).
Pottermore Chamber of Secrets
"The Chamber for the Teaching of Secrets" doesn't roll off the tongue so well.
It may also be that the name was devised after Slytherin's death, by those telling the legend of the Chamber. If so, it makes sense to use the plural form; they (presumably) don't know exactly what's down there, and surely a Darkly-inclined Wizard who went through the effort of constructing a secret Chamber in the bowels of Hogwarts would want to store more than one Secret in it, right?
What those other secrets could be, though, is unclear; we don't spend a whole lot of time in the Chamber, and the only thing that we see in it (other than the basilisk) is the enormous monument to Slytherin's ego:
[A] statue high as the Chamber itself loomed into view, standing against the back wall.
Harry had to crane his neck to look up into the giant face above: It was ancient and monkeyish, with a long, thin beard that fell almost to the bottom of the wizard’s sweeping stone robes, where two enormous gray feet stood on the smooth Chamber floor.
Harry Potter and the Chamber of Secrets Chapter 17: "The Heir of Slytherin"
