I'd go with “swap” and “swapped.”
Amending that: watch out for unintended ADL effects with “swap.” It's one of those globally claimed names whose meaning (at least with two arguments) is fixed for all time w.r.t. unqualified calls.
I think the consensus was to use "endian_cast" for the function which returns a swapped copy of the underlying data and "endian_swap" for the function which performs the swapping in place (Rob's suggestions). This is so that people can do using namespace boost::endian; int i = endian_cast<from_big>(j); which seems pretty readable. The only thing remaining for me to decide whether "endian_cast" and "endian_swap" should live in the endian namespace (as I indicated above) or in the boost namespace, as others have suggested. Even though I dislike the endian::endian_cast<> syntax, my personal preference would be to have endian_cast in the endian namespace for "cleanliness" issues - I may well be ok with using namespace boost::endian; in my local scope to but I will not be ok with doing using namespace boost; Tom