The "once per game" restriction seems odd to me. Why not effectively grant flashback/slow unearth to cards of the chosen name? That avoids the issue of just casting the same spell over and over again, but still rewards going deep on that spell. To clarify: "You may cast cards with the chosen name from your graveyard. If it's a permanent card, exile it if it would leave the battlefield. Otherwise, exile it as it resolves."