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Hold on.  We're conflating issues here.

To address the privacy issue, "localhost.localdomain" should
be used.  I don't see anything else being an appropriate
defense against identity leakage (but IMHO, it's a limited
defense anyway because you'll *always* leak your IP address)

To be "correct" IMO means adhering to RFC 2821 as closely as
is possible.  Which means use the fqdn if available,
otherwise use the domain literal.  See attached patch for that.

If we don't want to be RFC-correct but we want to be liberal
enough to handle misconfigured client systems, then
gethostname() is probably fine, but so would be
localhost.localdomain.

If we want to be robust in the face of overly strict smtp
servers, then I think you're in a losing battle because they
may only accept fqdn's that are reverse resolvable.  But
that may be impossible for the (perhaps misconfigured)
client to calculate.  And if that's the case, then the
client likely has bigger problems.

My preference would be for the default to be RFC-correct
(i.e. fqdn w/domain literal fallback), and allow overrides
via method arguments, as the code with my proposed patch
would implement.