I'm thinking they didn't want to add another company name in case that partnership ever ends, then they would have to change the name again.
I wish they had just called it Disney Studios. Just because Disney Hollywood Studios is so long and DHS doesn't roll off the tongue as easily as MGM did. I think they probably wanted to play up the 'hollywood' connection given the streetmosphere characters, street names, restaurants, the whole movie connection. I find myself calling it 'Studios' instead of DHS or the whole long name.