According to Kripke, proper names, like Barack Obama, Michael Jackson etc are rigid designators. In all possible worlds, the name refers to the 'object' Barack Obama or Michael Jackson. This is true for all real persons. But what about fictive persons? Like Mickey Mouse? What would Kripke say about fictional proper names?
Kripke hesitates a little bit when it comes to fictional entities. The issue partially boils down to the following question: "Could fictional entities like Sherlock Holmes and Mickey Mouse exist?"
On the one hand, you might think "Yeah, of course! Sherlock Holmes isn't contradictory or anything; surely there's a possible world where he could have existed." This was something like Kripke's old view. On the other hand, you might think, "No, Sherlock Holmes is a purely ficitonal character. Even if we were to discover that there was a man who actually did all the same things that Holmes did, and was even called Holmes, but (let's say) was completely unknown to Doyle, still the Sherlock Holmes of Doyle's stories would not be that person. Hence no possible person could be that Sherlock Holmes." This is more like Kripke's revised view.
In Naming and Necessity, Kripke has the following quote:
Similarly, I hold the metaphysical view that, granted that there is no Sherlock Holmes, one cannot say of any possible person that he would have been Sherlock Holmes, had he existed. Several distinct possible people, and even actual ones such as Darwin or Jack the Ripper, might have performed the exploits of Holmes, but there is none of whom we can say that he would have been Holmes had he performed these exploits... I thus could no longer write, as I once did, that 'Holmes does not exist, but in other states of affairs, he would have existed.' (p. 80)
If this is Kripke's view, then it seems that names of fictional characters would have to be treated differently from names of actual people. (Maybe this applies to merely possible objects too, but perhaps Kripke could argue for some notion of stipulating names for those kinds of objects.) This gets into a lot of tricky issues with regards to the philosophy of fiction. Generally, people set aside the issue of fictional objects in hopes of getting the theory without fictional objects right first; but the point you raise is an important one.
This is just a possible answer which another world may be the exactly right answer:
Presumably it could designate another fictional character like Sherlock Holmes. I suspect Kripke will have category distinctions for all objects in a world to prevent designators slipping from one category to another. We wouldn't want the Queen of England to become the Sesame Street, Cinderella, the great Barrier Reef or the mote in my eye.