The name bitcoin would always dominate over satoshi just like the US dollar and cent. Most people are not comfortable with quoting "Satoshi" when dealing with small amount of bitcoin. Personally, I prefer saying bitcoin instead of satoshi irrespective of how small the amount or bitcoin.
Many currencies have a different word for the unit of a currency. For example Sterling is the word to describe the Britsh currency, and it has a variety of units within that - The Pound, Pennies, Sovereigns, Britannias and Guineas. The Pound and the Penny are the most common ones, and mst people don't know of the others. The Chinese currency is known as the Renminbi, but most people seem to use the Yuan, which is the trading unit. The difficult with Bitcoin is the massive gap between the Satoshi and one Bitcoin, and one can only assume that Satoshi's vision was for Bitcoin to achieve such a stratified value, that the Saroshi became the practical unit of exchange.
Once you move into the world of investment currencies, things can get a bit complex. For example, a gold Britannia has a face value of £100, and is legal tender in the UK.A single coin currently costs £1,320.09 ( it was sub-£1,000 not so long ago ). That is 132,009 pennies. Obviously public use will be based on the most convenient and univerally recognised denomination. My point ws that people may feel richer when they have 132k pennies rather thasn one Britannia. In fact this is not really a valid comparison, as a Britannia is minter from 24 carat gold,and thus has a high intrinsic value. The penny is manufactured from base metals, and thus has a value related to the fiat currency. I believe that Bitcoin will become an investment unit, raher than a trading unit in ther future.