There are recipes for savory cheesecakes. I made one once a long time ago. I don't remember the details and I'm not a huge cheesecake fan but I think it turned out pretty good. I'm sure recipes abound on the internet.
The thing about the onion/chive flavored cream cheese, though, is that you would never use that in a cheesecake, not because of its flavor, but because it's whipped. You need the actual cream cheese bricks to make a real cheesecake. Then you add whatever flavorings, sweet or savory, according to the recipe, as required.