It would be difficult to think of the IDS as anything else.
It would be like calling the Empire State Building the Kong Plaza, or the Chrysler Building rebranded as 1 Pointe Centre, or the Sears Tower renamed something dumb, like Willis.
If the IDS were renamed, everyone would still call it the IDS. (See also, Willis Tower, Sears, new name of.)
Longtime residents get stubborn about these things. We may say the new name when giving directions, but we'd think the old name.
Eventually, some people would use the new name, but only the younger people who didn't grow up with the old name. Or the older people who just moved here, and outed themselves as non-natives at a dinner party by casually calling the IDS by its new name.
When it comes to buildings, especially big downtown buildings, name changes can be more than annoying, they can be downright confusing. (Take our quiz here.)
In the early days of the skyscraper era, the buildings were advertisements for the companies that commissioned them. But even back then, not all buildings got lasting names. In New York's 1920s building boom, for example, some towers were built on spec. They often got a street number for a name.
We've seen a lot of numbers as names in the Twin Cities, as name changes. The volatile real estate market means names come and go. Tenants change, and new owners want to tell the world they own the joint (or at least part of it).