Is this the correct way of moving MySQL data directory, (on Centos)?
Ideally you would keep that folder, and instead of changing it you'd either mount another folder or partition on it prior to starting mysql, or create a symlink elsewhere (there are answers for doing this here and here).

You won't need to rebuild anything for moving your files, but it is a good idea to always make a backup before attempting something like this that may damage your data if anything goes wrong.