This is what they're (Infinit) are already doing, isn't it? I can see why they might be a little annoyed at the name Infinite, but it's not like infinite is an unreasonable name for Dropbox to pick for their project...
Reasonability of the name has nothing to do with whether or not Dropbox can use "Project Infinite". That's the point that Dropboxe makes. Dropbox can either fight that name (which really, they must or lose their own mark meaning anyone can use "Dropbox") and lose their Project Infinite name as well.
What about "Windows"? Or "Word"? Or "Office"? It's difficult to find words that are more "mainstream" than that. Yet, Microsoft does just fine.