People often ask how Kafka got its name and if it signifies anything specific about the application itself. Jay Kreps offered the following insight:
I thought that since Kafka was a system optimized for writing, using a writer’s name would make sense. I had taken a lot of lit classes in college and liked Franz Kafka. Plus the name sounded cool for an open source project.
So basically there is not much of a relationship.
I feel like it's origins in LinkedIn, the performances people are expected to put in there, and the fact that it runs on a virtual machine, often on a cloud machine make the irony too great to be believable.