Responding to this question reminded me of something I have been trying to work out how to do for a while.
At the moment I just have one SO/SX account with one OpenID and both work and personal accounts all linked together. This is easy and simple, but means that during the day I get Inbox notifications for things which I only want to deal with out of work hours. Similarly, at home I get notifications for things which I want to deal with at work.
So, I'm considering trying to separate my work and personal Stack Exchange worlds, but I'm not even sure if this is possible now the accounts are all linked, without creating all new SX accounts.
I suspect that at the very least I will have to create a new OpenID with a different OpenID provider, add this openID to all of my personal accounts, update my display names on all of those accounts and then remove the original OpenID from them, but what else might I have to do?
Will switching them to another OpenID be enough? Or will the accounts all still be linked together? Has anyone done this, and if so, are there any issues I need to consider?
Note, I'm aiming for the two sets of SX sites to be completely disjoint. No site in my professional account will also be in my personal account and vice-versa, so no problems with appearing to be a sock-puppet. Also, obviously, I don't want to have create entirely new accounts for the SX sites I consider personal and have to start acquiring rep on them from scratch.