I'm not sure I want to help anyone regain their faith in Adobe after the terrible DRM infrastructure they have imposed on the world but refuse to support.
Also, the designers of ADE (if there were any) obviously hadn't attended 101 in interface design and learned about discoverability: so the feature you want is well hidden.
However, try ctrl-shift-D to ADE while it is running (cmd-shift-D on Mac). This will remove your old 'anonymous' ID.
Restart ADE and you should be able to register with your correct Adobe ID.