Like "cloud computing", the name "serverless" doesn't make much sense when used literally. It doesn't mean that there are no servers involved, just that there are none to be directly managed by the developer.
P2P also doesn't mean "no servers", but that every node is as much server as client.
Amazon popularized but didn't invent the term "serverless", which appears to have been first used in 2012.[1]
[1] http://readwrite.com/2012/10/15/why-the-future-of-software-a...