While the name bzip3 itself would be okay for reasons others stated, I still don't like it because it is so easy to confuse with bzip2 and may indicate a false

While the name bzip3 itself would be okay for reasons others stated, I still don't like it because it is so easy to confuse with bzip2 and may indicate a false relationship with bzip2 regardless of intents. A spiritual successor doesn't have to be named confusingly similar, after all.