There different ways to do that.
If you can change MyDTO class the simplest way is to add a setter as suggested by M.Deinum :
public class MyDTO { 
       private String kiosk;
       ...
       public void setNew_kiosk(String kiosk) {
           this.kiosk = kiosk;
       }
}
That way, you can process http://localhost:1234/mvc/controllerUrl?kiosk=false as well as http://localhost:1234/mvc/controllerUrl?new_kiosk=false
If you are not allowed to do that (because the DTO is part of a library you are not allowed to change or ...), you can use a filter mapped to /mvc/controllerUrl, that would wrap the request with a custom HttpServlerRequestWrapper that will override following methods : 
String  getParameter(String name)
Map<String,String[]>    getParameterMap()
Enumeration<String>     getParameterNames()
String[]    getParameterValues(String name)
calling the underlying request methods and processing the special parameter name. Example : 
String[]    getParameterValues(String name) {
    String[] values = req.getParameterValues(name); // req is the wrapped request
    if ("kiosk".equals(name) && (values == null) {  // will accept both names
        values = req.getParameterValues("new_kiosk"); // try alternate name
    }
    return values;
}
This will be much harder to write and test, so only go that way if you cannot modify MyDTO class.
You could also try to use a custom implementation of WebBindingInitializer. From Spring Framework Reference Manual :
To externalize data binding initialization, you can provide a custom implementation of the WebBindingInitializer interface, which you then enable by supplying a custom bean configuration for an AnnotationMethodHandlerAdapter, thus overriding the default configuration.
Beware : the recommended usage of that is to register custom editors for a whole application - not your use case. And Spring Framework is oftern described as easy to extend but not to override. Caveat emptor ...
Summary : try to use method 1, if you cannot, then use method2, and only try method3 if you have other reasons to use a custom WebBindingInitializer