The standard way to do this is to store $1 in a variable, then use shift to remove it from the argument list, and then use "$@" to get all of the remaining arguments (i.e. the original "$2" "$3" "$4" ...) Something like this:
RenameTo="$1"
shift
echo "New name: $RenameTo"
echo "files:" "$@"
I'm not sure exactly what you're trying to to with exiftool, so I won't try to give that full command.
Note that the double-quotes aren't required in zsh, but they make this portable to POSIX-compliant shells. Also, echo isn't a very good way to see what a command would do, because it looses the distinction between spaces within an argument (e.g. spaces in the new name, or within a filename) and spaces between arguments (e.g. between the filenamess in a list of them).
shift, but note that the names and paths should be quoted or characters special to the shell (such as space) escaped.