Find all files (type f) up to 3 levels deep (maxdepth 3) and execute the command to move (mv) them with the option to overwrite existing files (-i) to the destination directory (/mnt/dest/) with the name file_8, file_9, etc. (seq -f /mnt/dest/file_%g 8).
find . -maxdepth 3 -type f -exec mv -i {} $(seq -f /mnt/dest/file_%g 8) \;