It shows up as hostname.ipadomain in FreeIPA (which doesn't match its name on the networks) and I've never had any issue- I suspect client hostnames are not really important.

Sorry, correction. My laptop's hostname *IS* hostname.ipadomain. When it connects to different networks, the DNS servers there resolve that hostname in their domain, though, but I don't think the laptop is "aware" of that, although it has a new search domain in resolv.conf...