A customer was seeing some unusual behaviour a couple of weeks ago - they had installed a server site on a new server, and had placed their config store onto a shared storage partition. However the site seemed to pick up the config store details from another site - which was on another partition of the shared storage. The two config stores were different versions and had different content in so this very much confused the site! They tried renaming the site to something else completely (Jeff, if I remember). But it still seemed to pick up the other config store.
Would you have anticipated this behaviour? Even if they were named the same thing, it is surprising to me that it was still able to 'find' the other config store in preference to the one that was set. It causes problems if this is common as we need different storage for each test site we might set up.
I wouldn't consider this behavior expected. I'd log a case with Esri Support detailing your Enterprise GIS version, shared storage configuration, etc. so that this can be tested in-house.