1 satoshi  =  1e-9 BTC (since it/he doesn't really exist)

0.001 BTC = 1e-3 BTC  = = 1 millibitcoin  =  1 million satoshi  = 1 mill


I propose "1 mill"


we can have two camps one going to the left of the decimal, the other to the right and things can be thoroughly confused (and conflict with abbreviated millilitres and milligrams) but they will both agree on the mill.