Leaving academia - what to do with the personal website?
Put your website on some other hosting than your university.
Write up-to-date status and contact, perhaps with a few words of explanation (e.g. to make it clear that is not only for archival purposes).
When it comes to rest of stuff, they can be the same. (Minding academic data and contact; when it comes to branding - it is a question for Workplace SE and answers will depend on your profession.)