Editing the transcript
How do I fix a word the transcription got wrong?
Select the word and choose Correct, then type what it should say. This fixes the transcript, the captions and the exported text — it does not change the recorded audio, which still says what was actually said.
That distinction matters and it is worth stating plainly: correcting text is not re-recording. Cast does not synthesize a new word into your voice. If you want the audio itself to say something different, you have to record it.
For a name or a term the transcription gets wrong the same way every time, use Find & Replace instead of fixing each one.