A general comment – and with all due respect, you may wish to research jailkit Pros and Cons – there are other forum postings about issues and challenges when using it.
Each sysadmin has a different environment – I myself have never had a reason to use jailkit.
I’m surprised this would mask hostname, but, I’ve never used it and the purpose of jailkit is to be restrictive. I wonder if this particular behavior is something that would change from distro to distro depending on packagers?