How to tell which file is original if hard link is created

cp -p filename filename.tmp
mv -f filename.tmp filename

Making it scriptable:

dir=$(dirname -- "$filename")
tmp=$(TMPDIR=$dir mktemp)
cp -p -- "$filename" "$tmp"
mv -f -- "$tmp" "$filename"

Doing the copy first, then moving it into place, has the advantage that the file atomically changes from being a hard link to being a separate copy (there is no point in time where filename is partial or missing).

Don't do this. If you want to have a backup system using hard links to save space, better to use rsync with --link-dest, which will hard link files appropriately to save space, without causing the problems that this causes (that is, hard linking between directories is a corruption of the filesystem, and will cause it to report wrong inode counts + fail fsck + generally have unknown semantics due to not being a DAG).