Jay Kreps, the author of Apache Kafka says about the Kafka name:
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.
Apache Kafka is mainly optimized for writing (in this book when we say optimized we mean two million writes per second on a commodity cluster).
Nowadays, real-time information is continuously generated; this data needs easy ways to be delivered to multiple receivers. Most of the time, generators and consumers of information are inaccessible to each other, and here is when integration tools are required.
In the eighties, nineties and two thousands, the large software vendors (IBM, SAP, BEA, Oracle, Microsoft, Google, and so on) found a very lucrative market in the integration layer. Here we can find enterprise service buses, SOA architectures...