If the targeted player has multiple cards with the chosen name in their hand, the damage dealt by Thought Hemorrhage is all considered to be the same instance of damage. A single effect that prevents “the next time a source would deal damage,” for example, will prevent all of it.

Thought Hemorrhage has no effect on cards on the battlefield that have the same name as the named card.

The card is named as Thought Hemorrhage resolves. Spells and abilities can’t be cast or activated between the time a card is named and the time that Thought Hemorrhage has the rest of its effect.

The cards you’re searching for must be found if they’re in the graveyard, because that’s a zone everyone can see. Finding those cards in the hand and library is optional, though. This is true even though the targeted player has revealed their hand.

If you target yourself with this spell, you must reveal your entire hand to the other players just as any other player would.