How can you tell that you have not added enough NaOH to precipitate all the copper as copper hydroxide?

Are you titrating? Qualitative testing? Just what? If the copper is in solution you can filter the ppt (or let the ppt settle and decant some of the supernatant liquid) and to the filtrate or the decanted liquid add some more NaOH to see if additional ppt will form. If I have guessed wrong about the application just clarify what you're doing and repost.