Regarding the name - how about adopting MAP_EXCL?  It was introduced in
FreeBSD,
and seems to do exactly this; quoting mmap(2):

MAP_FIXED    Do not permit the system to select a different address
                        than the one specified.  If the specified address
                        cannot be used, mmap() will fail.  If MAP_FIXED is
                        specified, addr must be a multiple of the page size.
                        If MAP_EXCL is not specified, a successful MAP_FIXED
                        request replaces any previous mappings for the
                        process' pages in the range from addr to addr + len.
                        In contrast, if MAP_EXCL is specified, the request
                        will fail if a mapping already exists within the
                        range.