Remember, variables are REFERENCES to objects. Variables are not objects themselves.
Setting secondName to null means that it is a reference to no object. No methods may be executed using that reference (you'll get NullPointerException if you try).
Setting secondName to "" means that it is a reference to a zero-length String object. Any method of the String class may be executed using that reference. Java will ensure that only one such object gets created, no matter how many times you use "" in your program (literal Strings are 'interned').
Betty Rubble? Well, I would go with Betty... but I'd be thinking of Wilma.