Are the legendaries Prince Malchezaar adds to my deck all different?

Solution 1:

Prince Malchezaar follows the Deckbuildung rules, which means that

• no legendary that is already in your deck is added
• five differerent legendaries are added
• no legendaries of other classes are added

Source

As @CobaltZorch mentioned in the comments, Prince Malchezaar adds the cards after the mulligan. This makes it possible that a legendary that you already have in your hand is added to the deck. The legendaries in your deck will stil be unique though, so Reno etc. will still work without surprises.

Solution 2:

Prince Malchezaar will not add duplicate legendaries to your deck, so it is safe to play Reno in your deck. It will also only add neutral and the same class legendaries to you deck.

Source: https://www.reddit.com/r/hearthstone/comments/4vm13p/reveal_2_new_cards_revealed_by_ben_brode_in_s/ (Reddit post about Ben Brode announcing the card)