Using a variable as identifier in a json array

You will need to build your object in two steps, and use the [] property accessor:

var parameter = 'animal';
var value = 'pony';

var obj = {};
obj[parameter] = value;

Util.urlAppendParameters (url, obj);

I don't think JSON Array is the more correct term, I would call it Object literal.

No, you can't use a variable as an identifier within an object literal like that. The parser is expecting a name there so you can't do much else but provide a string. Similarly you couldn't do something like this:

var parameter = 'animal';
var parameter = 'value'; //<- Parser expects a name, nothing more, so original parameter will not be used as name

The only work around if you really really want to use an object literal on a single line is to use eval:

Util.urlAppendParameters (url, eval("({" + parameter + " : value})");