Ebondeath, Dracolich's last ability cares only whether a creature not named Ebondeath, Dracolich died during the turn, even if Ebondeath, Dracolich wasn't in your graveyard when that happened. It doesn't matter if a creature named Ebondeath, Dracolich also died, and it doesn't matter what happens to the creature after it dies. For example, if the creature that died is a token or the creature card leaves the graveyard later in the turn, you can still cast Ebondeath, Dracolich.

Casting Ebondeath, Dracolich from your graveyard follows the normal rules for casting that card. You must pay its costs, and you must follow all applicable timing rules.

Ebondeath Dracolich cares what the creature's name was while it was last on the battlefield, not what it is in the graveyard. For example, if a creature with a different name becomes a copy of Ebondeath, Dracolich and then dies, you won't be able to cast Ebondeath, Dracolich from your graveyard.