If you want to do anything with your GoDaddy account, you will need to use the Customer # they give you. It will allow you to reset your password, use phone support, and allow domain pushes to your account. Thankfully, it isn’t too difficult to find.
As soon as you log in to your account, you can click your name in the top right-hand corner. Your number will be there. Please make sure you write it down, because if you end up being unable to access the dashboard for any reason (e.g., you have forgotten your password), then you will never be able to see this number again!
There is no real need to keep your customer number secure. If you are buying and selling domains, you won’t be able to do so anyway. It is because nobody will be able to log in to your account or change your password with your customer number alone. However, as with any personal data, try to keep it as secure as you possibly can do.