The specific term is: parameterized factory method and it is part of the factory method design pattern.
To use a generic factory, hold the classes in a map and access via a string. If your class names are usable, register the class to the factory with "typeid(MyClass).name() and return a copy of the class by providing a clone() member function.
However, for simple not to extensible factories, I use the approach from your question.
I can't answer your question about passing more variable parameters, but to deserialize, it is enough to pass the portion to the class and let it deserialize itself (as you already seem to do).
