There are also a whole lot of Indonesians out there who probably want
their island back from Sun. (Though the way things are in Java right
now, the residents would probably be happier with a licensing deal).
Sun, for that matter, is the name of a big glowing round thing in the
sky as well as being the name of a company. And Sun is in the same
industry as Apple, which is named after a fruit, and has gotten into
trademark disputes with a music publisher of the exact same name in
Britain (the Beatles' old private label).
The thing to remember, as in the Apple v. Apple case, is that
trademarks are, by and large, *specific to a particular industry*;
the rationale for having trademark law at all is simply to prevent
confusion among customers, and trademark disputes frequently hinge on
whether mentally competent customers would actually be confused.
Apple Ltd. made no moves against Apple Computer so long as the latter
stayed out of the music business; the dispute was over some
Apple-branded products for musicians.
Likewise, it is probably not kosher to trademark Apple as the name of
a fruit, or Iridium as the name of some new metal alloy, but as
computers or communications networks, they're fine (so long as no one
else in the same, or some closely related market segment was already
using the marks).
At least that's my understanding --- but then again, if you need real
legal advice, you should of course consult a real lawyer.