Is there an easy way to duplicate a class with a different name?
Not sure whether this can be qualified as the easiest way but if you have ReSharper, you can use its Copy Type refactoring to copy classes/interfaces/structs with control over the namespace the copy is landing in and naming within the copy - which means that if you're copying a class with 5 constructors, the copy will have all of them renamed to match the name of the new class.
However, depending on what you're trying to achieve, using Extract Interface or Extract Superclass might be a better option.