How to pass parameters in eval in an object form?

Depends on where the function to call is defined (global scope or a local scope).

If global, you don't need eval (and it's safer to avoid it), you just reference the function through the global window object:

var args = [];
for(var p in json.callback.callbackParams) {
    args.push(json.callback.callbackParams[p]);
}
window[json.callback.callbackName].apply(null, args)

See the apply() function used above.

If it's in a local scope, then you need the eval (how you have it is fine).

Don't use eval. You can get a reference to a named global variable or function from the window object:

var callbackfunction= window[json.callback.callbackName];

And trying to serialise your values to a string just to have them parsed back to JavaScript unreliably is silly. Call the function explicitly:

callbackfunction.call(window, json.callback.callbackParams.param1, json.callback.callbackParams.param2);

(window here is a dummy value for this for when you're not using object methods.)

Better for automating it to accept any number of parameters would be to turn callbackParams into a plain Array:

callbackParams: [1, 2]

and then use apply to call the function:

callbackfunction.apply(window, json.callback.callbackParams);