"Whenever I set up an iPad or iPhone for a new user, they figure out where email, phone, contacts, calendars and so forth are, but the web? That one confuses most people, because “Safari” isn’t something they are used to calling the Internet.
I very much like the idea of giving users a better understanding of what things do by using verbs instead of brand names — I think it is a natural extension of this post-pc hoopla people are caught up in."
This is an interesting idea, although I don't think I'd like it very much myself.
Let's say every smartphone brand began using 'Connect' in place of their previous browser names. We'd have to refer to these things as Apple Connect rather than Safari, Microsoft Connect rather than Internet Explorer, Google Connect rather than Chrome, etc. It would be the only way of telling them apart in discussion, and they actually are quite different products so there would be no avoiding it. Sounds like more of a pain than it's worth.
I wouldn't want to take away names of mail clients either, since some of them are so ingrained in tech culture, Outlook and Gmail in particular. 'Apple Mail' is admittedly kind of generic, but people have seemingly accepted it so I'm ambivalent there.
Perhaps a better way to help new users find the 'Internet' app would be changing the icon rather than the name. If I didn't already know what these logos represented, I don't think I would be able to immediately tell that they were for accessing websites. At least the icons of mail clients usually contain some sort of envelope metaphor, regardless of their name.