there are 2 different systems for managing your model(s); the C4R space and the A360 space - both are not the same.
you control/manage models in the C4R via the 'Manage A360 Models' button in Revit; you can rename, delete, relinquish, etc...
you control/manage models in the A360 space via the A360 Team Hub web site https://the-name-of-your-team.autodesk360.com
You can publish the model(s) from the C4R space to the Team Hub Space (A360 Team Hub) via the publish operation from the 'Manage A360 Models' button in Revit.

The icon that looks like a blue box with an upwards arrow, is the icon you click-on to publish your model to A360 Team Hub.
(forgot to mention)
C4R can only have a unique name for the model(s). if you want to maintain the same name of a new version (of the model), then you will need to delete the existing model on the C4R side, then re on-board the model to the C4R space.
Currently, there it's not possible to put any .rvt file into the A360 Team Hub and have it convert to a C4R model automatically. that would be nice, but probably not anytime soon. You could think of the A360 Team Hub as sort of an on-line archiving mechanism where you maintain archives of your model(s).
Hope this helps to clear things up a bit. it seemed a bit confusing at first on our side, then it became more clear the more we, and our consultants, worked with both services.