Is it sufficient for a worshiper to change their intention during a prayer that they started with the intention of Dhuhr, then remembered in the second rak'ah that it was the 'Asr prayer, or should they interrupt the prayer, or repeat it, knowing that they completed the prayer with the intention of 'Asr?

If what happened was a whisper (waswasah), then pay no attention to it. However, if you are certain that you intended the Dhuhr prayer, then your prayer is not sufficient for the Asr prayer, because the intention for Dhuhr is not valid for the Asr prayer. You should have interrupted the prayer and restarted it with the intention for Asr from the beginning, then made up what you missed. Since you did not do that, you must repeat the prayer.