"Determined" would be an antonym for "denominated." It means having made up one's mind completely or firm in purpose. Other antonyms could include "undecided" or "uncertain," meaning lacking a definite determination or just not knowing what to do or how they feel about a particular choice. "Uncommitted" also works as an antonym, which describes someone who has not yet pledged loyalty or promised support to any particular party, team, or cause. Finally, "undesignated" or "unspecified" could also be used, meaning things are not assigned or appointed to any particular role or category. These antonyms for "de nominated" showcase a range of possibilities from being uncertain to entirely determined.