Thanks for the input @scotru! Maybe I should have contacted or mentioned you more directly from the beginning, but I'm glad you bumped in and provided that explanation. It can really be a mess, if display and usernames are different. I accepted your answer instead, since that was of course the best ;-)

Well, maybe it's just the user profile, but never mind now. And thanks for joining and looking at the issue.

Ah, thanks for reminding me about DSRM, but I think you missed one thing. As far as I remember, the local admin account used to install AD, is copied or "converted" to a domain user and the "original" is preserved in DSRM, so it becomes two separate accounts (and profiles). There is at least always a "default" Administrator account in the Users folder in the root of the AD, with the description "Built-in account for administering the computer/domain".

Thanks for the input, I learned a lesson and changed my mind. I have improved both the question and answer to be more usable.