The general rule is that if a command operates on links (i.e. directory entries, which are pointers to inodes) then the command treats symlinks as themselves rather than as the object the link points to. Otherwise the command operates on what the symlink points to. Thus
cp follows symlinks by default and copies the contents of the file pointed to by the link. But when you ask
cp to deal with directory entries by specifying
-R, it stops following symlinks.
mv always works with directory entries, and so it never follows symlinks.
find command's normal activity is to operate on directory entries, so symlinks are not followed by default. Adding
find to follow symlinks for all properties except the one that cannot be ignored when doing directory search, the name. One of purposes of
find -name is to provide input for commands like
rm, which operate on directory entries. There would be unpleasant and surprising results if
find -L dir -name could produce names that pointed outside the directory tree rooted at