Board Thread:General Discussion/@comment-2028390-20130704093733/@comment-8986886-20130704154736

I agree that the old man took the name Zangetsu from Hollow Ichigo to use as an alias, however the old man has continuously answered to that name ever since his first talk with Ichigo, years ago.

Taken or not, that's the name he's been using all this time and until he chooses a new name, they should both be referred to as Zangetsu.