I just did this. First, go to your existing account and change the email address associated with that account to something else, like maybe a gmail account. Save that update. Then go to the Houzz main page and sign up for a whole new account with the url you want to re-use. You'll need to create a new user name as well.

Like me, you may have the additional step of changing the company name on that existing account. The field will be grayed-out so you won't be able to do it on your end. Email the folks at Houzz to do it for you, they are very helpful.