I'm waiting for the signs to go up for the theory to take full effect. People will see these big signs facing them saying "Toronto Life Square". There doesn't seem to be a Yonge Dundas Square sign anywhere.
Once the name becomes ingrained, it will be natural for locals to drop the "Toronto".
I think people won't associate the "Toronto Life" part to the magazine. I think they'll see "Toronto Life Square" (Life Square in Toronto). I for one didn't know that Times Square got its name from the publishing company until I looked it up.
Currently, my non urban geek friends don't know where or what Toronto Life Square is. I have to say the "AMC across from the Eaton Centre".