@vmedea And that didn’t work either. I need to look into that in more detail later.
The Referer HTTP header and the User-Agent HTTP header are two completely different things.
I just did a test of both Safari and Firefox on a spiPhone and in neither case did the User-Agent leak the name of the phone. For sure, the User-Agent leaks lots of information that would be useful to a would be intruder - but not the name of the phone. Software is fairly current - so I can’t rule out the possibility that an earlier version of iOS did leak the name of the phone via the User-Agent.
There are some cases where if the Referer is leaking anything at all then that would be a serious implementation error on the part of browser. There are other cases where the Referer might legitimately leak things that it ought not - but I didn’t test whether either browser takes steps to address that. In any case the Referer is supposed to be a valid URL, relating to the browsing, and so does not randomly leak information (unlike the User-Agent string, which can leak arbitrary information).
I can more believe that a mail client (for outgoing mail) could leak a hostname or other information that people may not intend to leak.
Either way, I suggest you look again at what really happened.
This discussion is only relevant to leaking your hostname to a DHCP server. So, where the DHCP server is your own (device at home), that shouldn’t be a concern - unless the DHCP server itself is leaking. DHCP may be more of a concern for portable devices, using untrusted DHCP servers. (Hence a mobile phone might leak the hostname to your mobile service provider - and any portable device using an employer or public WiFi might leak the hostname to the provider of the WiFi.)