Before decimalisation, names of coins in Britain included: penny, tanner, shilling (also known as a “bob”), florin, half-crown & crown
Names of coins in the US: penny, nickel, dime, quarter. Although US currency is decimal, the nickel and quarter are non-decimal divisions, echoing the British practice - a nickel is a 20th of a dollar, like a shilling is a 20th of a pound, and a quarter-dollar replaced the crown, which is a quarter of a pound.
My point being that, in non-decimal systems, units have names and “identities”. Thus, an inch is an independent unit, as well as being a division of a foot. One is not senior to the other. Similar with time: a “minute” has its own identity, quite distinct from a “week”.
Traditional systems have these names because they evolved, from the ground up, over centuries. Each unit has its own purpose and, as Cybnate says, names just appear and catch on
Decimal systems or, more accurately, milli-systems, are created much more quickly, virtually overnight in historical terms, and so the smaller units have no separate identity - they are sub-divisions (or multiples) of a base unit, preceded by micro-, milli-, centi-, mega-, etc.
If the peercoin system developed “naturally”, no one would dream of thinking in terms of “500-thousands of a peercoin”, or “250 milli-peers” - people would simply talk in terms of half-peers and quarter-peers
We therefore have a difficult task, as we are creating, more or less instantly, a milli-system, but wanting to give sub-units “organic” names, normally associated with fractions and binary multiples (x2, x4, x8, etc.)
Another challenge is that we do not know how much a peercoin will be worth in the future. The reason for the poll (seeking a name for a millionth of a peercoin) is that we need names for milli-units now, to make the system usable if peercoin goes to $1,000.
I would argue something quite different: that if peercoin goes to $1,000 or higher, we should consider re-deploying the name “peercoin” to a more practical amount (e.g. $10). Peercoin is a good name, and it should settle at a level where people are likely to use it on a daily basis.
Many European countries have done this, knocking zeros off their numbers, so that instead of needing, say, 10 francs to a buy a pencil, the currency was adjusted so that it would take only 1 franc. It is an illusion, of course, the pencil still costs the same compared to everything else, but from a psychological point-of-view, it encourages acceptance.
I voted for peerbit as a name for a sub-unit, but prefer it as a hundredth of a re-scaled peercoin, rather than a millionth of a larger peercoin.