The Ontological Status of Jake Blues

In the airport, I noticed the cover of the latest issue of Cigar Aficionado magazine (not a regular read of mine) which features the Blues Brothers with Jim Belushi as Jake. Something felt odd about it and I've been trying to think through the case ever since.

On one hand, there is nothing strange about the identity of a fictional character remaining the same when played by a different actor. James Bond or Batman, for example, is the same character, regardless of who is playing them in any given film. Indeed, the Doctor in Dr. Who has the change of actor built in to the very character himself. Fictional characters exist in the fictional world of their story, they are intrinsically defined by the setting and plot in which they are created. When that world is brought to life in film or on stage, it is the character and not the actor who we see as "real" even if they do not have real existence in our world. As such, there seems no real problem here.

On the other hand, there is also not a problem with a band changing members and remaining the same band. The Grateful Dead were still Grateful Dead after PigPen's death, Tom Constanten leaving, Keith's death, and Brent's death. Replacing the keyboard player did not make the band something new, just ushered in a new phase of the band. As such, having a new singer should not make a difference.

But what happened here is a combination of these two cases and that is what is weird. The Blues Brothers exist in one sense as fictional characters in a fictional setting. On the other hand, they are a real band that plays real gigs. As such, we are left with the possibility of inferences like this:

Joliet Jake Blues sings for the Blues Brothers.
The Blues Brothers opened for the Grateful Dead at the closing of Winterland.
The Blues Brothers will be playing a show next week in Chicago with Buddy Guy.
Therefore, Joliet Jake will have performed with both the Grateful Dead and Buddy Guy.

That doesn't seem to work. It does not appear too different from the case of Charles Dodgson announcing that "his friend" Lewis Carroll is dead because he was tired of fielding questions about Alice in Wonderland.

How ought we make sense of the meaning of names that are not purely fiction and not purely real?