I believe what you should be using instead is the PortalRequestContext (use PortalRequestContext.getCurrentInstance() to get access to it). I think the portal name is retrieved through something like getPortalOwner
Yes, you could retrieve portal name via PortalRequestContext.getPortalOwner();
and for the returned ExoContainerContext.
getCurrentContainer().getContext().getPortalContainerName(), it would be corresponding to<my portal>/<page>
Yep - that did it!
Thanks for your help.