Well, the College degree will have the College name on it; the key was going to be if Holy Cross' has Hellenic College on it also (since Hellenic College is the name of the overarching corporate entity).
Indeed, it does, saying:
upon the recommendation of the Faculty of
GREEK ORTHODOX SCHOOL OF THEOLOGY
and the board of trustees
have conferred on
The City of Cleveland
With High Distinction
The Degree of
Master of Divinity
with all the rights..."
So Hellenic College, as the overarching institution, confers the degrees, upon the recommendation of the faculty of each institution (College and Theological School).
Boy is that scary, and not just the Cleveland part