The process name is
nautilus. Nautilus contains its own code to copy files, this code is executed inside the nautilus process, not in a subprocess.
You can see for yourself what subprocesses Nautilus runs by logging its system calls with strace:
strace -f -o /tmp/nautilus.strace nautilus
clone system call creates new processes (it's a generalization of
execve system call runs another program in the same process. Running another program thus entails
clone followed by
execve. You can quickly see what programs Nautilus executes (or tries to) with
grep execve /tmp/nautilus.strace
You'll find that Nautilus creates subprocesses for some things such as previewing the content of certain types of files, but it does the file copying on its own.