I was the one who proposed the name satoshi.

On 15 November 2010, in this post, I suggested calling 0.01 BTC a "satoshi". At the time, 0.01 BTC was the smallest unit that could be displayed by the user interface in the standard client, even though the protocol supported eight decimal places.

The discussion progressed, and on 10 February 2011 I proposed naming the smallest base unit (0.00000001 BTC) either an "austrian" or a "satoshi". In retrospect it's obvious that "satoshi" was the better name.

On 18 February 2011, marcus_of_augustus posted "100 million satoshis = 1 bitcoin. Are we agreed?" to which someone responded "affirmative", and the usage caught on.

Satoshi Nakamoto referred to the base unit simply as a "coin" in his writings.