As we are looking at upgrading our VLE from WebCT 4.1, we've been talking about rebranding it. This will mean that any changes in the future can be a little more transparent and all references to WebCT in documents wouldn't all need to be changed to for example Moodle, if we were to go that way.
Webteam called it 'myLearningSpace' on the portal. Personally I think this is a bit misleading as the VLE isn't your space, it's the teacher's space. 'Online Classrooms' would perhaps be more correct.
'myLearningSpace' would be better used to brand an eportfolio system like PebblePad, or a 'Personal Learning Landscape' like ELLG. These are actually spaces owned by the students.