I don't want to share my HBO Go account with the rest of my family.
Why did you make a family account then?
I just don't want to be the one to pay for the account.
Since you are the person who signed up and are the owner of the account, you have control and final say of who you can share your account with or not. If you do not want your family to use your account, that is well within your rights since the account is paid for by you.
I'm just going to change the password so so they won't be able to access the account. I want them to stop using my account.
Tell them then. If you do not want to share things like this, there is no reason that you need to.