Shane's answer is perfectly correct as to the question as worded, but I figure we could use some added background.
I think the question doesn't seem to grasp what Kripke means by rigid designator. A rigid designator by definition is a term that picks out only one thing and continues to pick out the same thing regardless of everything else. That is its definitional property. In this respect, it differs from non-rigid forms of designation like "President of the United States" or "my dog" or even "planet on which life exists."
Rigid designators are also thus always proper names but not every proper name is a rigid designator. Thus, "Jimmy" might be a proper name but it only rigidly designates when we declare "This is Jimmy" and attribute this to an object. As shane indicates, if we do so for multiple objects, we will need to further distinguish them which is tedious in normal language. But that doesn't represent a further challenge to Kripke's view.
In fact, it represents an affirmation. A major purpose of his account of rigid designation is to solve the naming problem faced by philosophy of language. The solution is to add to the account of acts of designation. From henceforth, we shall call this X. That means that rigid designator picks it out in all worlds. That doesn't mean that every world has to have given it the same conventional name -- just that the rigid designator continues to attach to the object regardless of what the thing is called.
Returning to Barack Obama, if we have assigned that to rigidly designate the Barack Obama who is our current president, then that picks out the same person in all worlds regardless of what he's doing in any of them (Messiah, Great Satan, Community Organizer, President, Lawyer, etc., etc.). It doesn't matter what name he goes by in any of the worlds either. What matters is that a rigid designator is by definition something that sticks to him -- not to his roles. If the same object is somehow a garden gnome in another world, that would be Barack Obama.
The "barack obama" garden gnome doesn't present a problem in the real world, because even if we make "barack obama" the rigid designator for the gnome and the same words the rigid designator for the current president, we've really just created to homonyms that are rigid designators -- rather than a conundrum. If they were mere names, it created a conundrum because it would not be clear how they pick out their objects (thus the problem Hesperus and Phosphorus)