That's an interesting question...
On the one hand, when MGM Grand Casino & Theme Park changed to MGM Grand Hotel/Casino (a minor change), both names are grouped together.
On the other hand, when The Quad changed to The Linq (though same ownership, etc.), its shown as 2 different entries. And filed under "Q" and "L" respectively.
Stratosphere changing to The Strat is somewhere in between. I would probably vote for a combined entry, but with a referral, such as "Strat, The -- see Stratosphere". I could be persuaded for the 2 separate entries option as well, though.