It is a proper noun, yes. However, you do still respect the tradename and never capitalize the i.
In formal writing, however, you need to avoid the oddity of starting a sentence like this:
iPhones are here to stay.
You do this by recasting the sentence:
It is clear that iPhones are here to stay.
The iPhone is here to stay.
The problem is not a new one. We've had it ever since e e cummings, and by the time he went out of style, k d lang reminded us of it.