"You have just freed the innocent spirit that this dark mask had kept imprisoned within the body of evil Odolwa."
That, I believe, is the in-game quote from after defeating Odolwa and obtaining it's remains. Similar text shows up for all the four bosses. The "innocent spirit" is most likely the Giant, and the text clearly states that Odolwa, and this applies to the other bosses as well, is the name of an evil entity who's purpose is to trap the Giant. If the Giants do have formal names, the boss names are not it.
EDIT:
"Do you think he was talking about the spirit that was sealed inside that mask?"
Is this the quote from Tatl that you were talking about? The quote itself simply implies that the Giants are trapped inside the mask, but the mask does not necessarily have to be named after them. The masks were just the hulls of the defeated bosses, thus named after the bosses, and Tatl commented that the Giant was sealed inside of the mask because the mask was all that remained of the boss's body, which the previous quote confirmed was the actual cage holding the Giant's spirit.