The movie would be the story of the cover band, not the original Blues Brothers. The roads of the two protagonists meet for some reasons in stand up comedy shows, where one day they discover to be able to perform like the original Blues Brothers. They receive a contract to make a movie like The Blues Brothers. So the film tell the story of the making of the new movie. But all the filming risks not to be completed because of all the enemies they have (criminals, police and so on). At the end they are arrested and they have still to perform the last scene. So the director decide to make the last scene from real, filming it into the prison where they are detained.
The name used would be the name of the cover band that at the moment I can't say. However it contains the two words Blues Brothers in itself (something life Blues Brothers Revival). But if needed we can change the name with something different that sounds similar.
Can I say in the film that they are fan of the original Blues Brothers (using these two words)?
Obviously the scenes and the dialog is completely different, but some people can see in the new movie some assonance with the old. Like the fact that here they receive a contract for a new movie, while in the old they received a contract for a LP. Is this allowed?