First, the term "bitcoin" gives me a sense of meh. The client is the only part of the bitcoin network that uses the name and it can be changed to any other name and it would still have the same value. This is useful for making fractional denominations with different names. In fact, rather than showing fractions at all, the client could show 0.00000001 "bitcoins" as single "Satoshis" instead and the client could be called a Satoshi wallet, for example.

Second, the term "bitcoin" gives the press a target of something they don't understand and fear. Calling crypto-currency by a single name is like calling anything that is printed, a "book." We all know how fast books can be banned and burned, even in "free" nations. This is the first "money" created of, by, and for the people-of-the-world. This is the first money of a Global Republic. There is just no name that describes how important this technology will become in the next few decades.

While I'm on the name rant, the term "miner" has gotta go. I prefer qikaifu's "auditor." Technically, since we are using Satoshi's original hash, we could simply refer to the bitcoin network itself as bitcoin, but I suspect that many branched versions are being created and will be adopted using the same network. This fact itself may confuse people if we get locked into a name without some established taxonomy being adopted.

On a side note: probably, every government will want a registered version of their own seeded branch used by their own economy, at least for awhile. This can be good for the growth of the network and allow sovereign nations to maintain some control of their economies. Of course, virtual wars will be fought on the network, but hey, that's who we are.

tl;dr
Bitcoin is too big to fail. It needs to be taken seriously and a naming convention taxonomy is in order.