I was thinking the same thing but in Google's case, Chrome is the dominate browser and most people recognize it as something they already have. In the case of Firefox, it's more likely they'll recognize the name specifically as the browser they don't have and will think they can't use it.
I think what helps is that there's two (or more) parties to a file transfer: the sender and the recipient. Someone who uses Firefox might start using Send, and then the recipient(s) finds out that they can use it too. And if they're using Send, the might start to consider using Firefox, or to create a Firefox account first.
