When you try to change the primary administrative user in the WebSphere Console in

Security > Global Security > Configure > Primary administrative user name

You get the following error message:

websphere primary administrative user id does not exist in the registry

This is because by default, WebSphere uses the uid property to fetch user instead of cn, used with Tivoli Directory Server. To change the way WebSphere search for user, in the same location, go to Additional properties > Advanced Lightweight Directory Access Protocol (LDAP) user registry settings, and replace:

(&(uid=%v)(objectclass=person))

with

(&(cn=%v)(objectclass=person))