So why algorithmic money? Why not crypto-currency or p2p money?
Well...
p2p is an old buzzword, and one used by bittorrent though. I even heard my bank manager call their bank accounts peer to peer. It's a common finance term now.
http://en.wikipedia.org/wiki/Peer-to-peer_bankingcrypto sounds shady to most people. Like crypto-jews or crypto-nazis. People who want to hide things. Also technically DigiCash was a crypto-currency (and centralised). Bitcoin's defining feature it uses code to self regulate in a decentralised manner without an authority.
emoney, internet money or digital cash sounds like paypal. Not at all new or interesting.
Algorithm is a neutral word. If someone doesn't know what it means, they will google it and get a good description.
Quote by Nick Szabo who made bit gold, one of the fore-runners to bitcoin:
And what's up with the term "cryptocurrency"? What is it supposed to mean? Cryptography is used to protect payments systems as radically different as credit cards, Chaumian digital cash, and Bitcoin. The term encourages the popular but profoundly naive view of Bitcoin as merely another form of digital cash.