Originally, the practice of putting the recipient's name on the letter,as well as the envelope, was that - should the envelope be accidentally damaged, for example by machinery in the sorting office - and its contents separated from the envelope - the letter could be re-packed and sent on its way.
In my days as a young post office worker (we're going back a long time now) there was a Returned Letter Section of the post office. I found it quite sad to handle letters that would never reach their destination (some folk don't bother to put their own name and address on personal letters, so they couldn't be returned to sender either).
Also, if you are sending a hand-written letter to a company (with a CV, for example) - the post might be opened by the post-room staff and forwarded on. If the recipient's name is on the letter, it's quicker and easier to direct it to the right person.
In regards to your question - I don't think there's a hard and fast rule, it's a matter of personal choice. I would centre my name and address at the top of the paper, then add the recipient's name and address at the left-hand margin.