HichiIchi is the name of the relationship between Ichigo Kurosaki and his inner hollow. So far in the manga, it has been confirmed that Hollow Ichigo was truly Zangetsu. However, for ship purposes, the fanon name "Hichigo" is still kept to prevent confusion.
Another name for this pairing is ShiroIchi, which is based on Hollow Ichigo's other fanon name "Shirosaki".
Soul Society ArcEdit
Fake Karakura Town ArcEdit
While it can never be canon in a romantic light, the dynamic between wielder and powers is canon by default. They are interdependent forces. Ichigo can't protect efficiently without powers and Ichigo's inner hollow is a part of Ichigo. Out of all the black vs. white elements present in the manga, this duo closely represents that dynamic the most, evidently with their color contrast outfits.