I don't think that a name change is going to matter. If you have an information commons and you can't show that it's providing good value to the institution that funds it, it's just as likely to be cut down or shuttered as a library in the same situation.
A public library that I worked for was on the chopping block a few years ago due to city budget cuts. While this was a nice enough public library, it wasn't exactly cutting edge. There was nothing like an information commons there.
The library was saved because patrons came out in droves to the meeting where the decision on closing it was to be made. People came and spoke about what the library did for them, what value it had, and why they couldn't get those same services elsewhere. One man spoke about how he learned to read through a literacy program that the library provided, and that he'd gotten the first job of his life thanks to skills he learned there.
Public perceptions of libraries are not what we want them to be - I once heard about a survey where college students thought, on average, that a librarian had about a high-school diploma-level education. On the other hand, individuals' perceptions based on experience are usually right on. If you're providing good service, people don't care what you call it, and they'll go to bat for you. If you're not, don't expect a huge outcry on closing day.