Blockchains are strongly anti-anonymity in their basic conception. A permanent record, publicly shared
*Perhaps not coincidentally, the old film Bob & Carol & Ted & Alice had unusual openness as a central theme.
is not the best basis for covering your tracks. Associations by assignment of shares are easily and automatically mappable. Shares on the blockchain themselves have no intrinsic value, so while they may be carefully masked behind random cryptographic keys, sooner or later the blockchain contracts are exchanged for something of real-world value, and those exchange points will very often unmask real-world identities. To build trust, traders in a blockchain may voluntarily securely identify themselves. Nonetheless, certain transactions can be anonymous, at least for a while. When Eddie sold Charlie his first 50 BCG, Charlie handed over cash and didn't provide any identity in the assignment contract beyond his public key. However, when that public key started exchanging BCG for CCC a couple of plates at a time, it quickly became apparent that Charlie bought the 50 plates and was selling them off.

Anonymity is also an opponent of the Web of Trust, and much of the value in a Web of Trust lies in its size and reliability. In Island Life when the only thing that Ziggy Credits would buy was BCG, they were a very hard sell. But, when a guest can pull up ZIC on their AOE and see a list of dozens of interesting vendors on this island, and hundreds more on their remaining vacation itinerary, all with prices listed in ZIC, that makes ZIC much more valuable to them. Referral agreements don't work well between anonymous partners, and anonymous players don't accrue trustworthiness as they play.

Guests and other buyers of goods and services might purchase credits for cash without revealing their identity, and even use an "untraceable burner phone" to spend them with, but that's still much more traceable than cash - all their transactions are easily linked and timestamped, if one of those transactions unmasks their identity it is readily linked to all other transactions they made from that initial cash exchange.

Bottom line: honest, long term traders on blockchains have much more to gain than they do to lose by freely publishing their
*secure and verifiable. Just because a transaction has a name or other identity on it does not in any way mean that that identity is accurate. Identities confirmed through use of well managed secret keys start to become trustable.
identity along with their transactions. Like a phone book when most people are listed, unlisted numbers stand out: begging for attention. Short term users of blockchains may choose to not share their identity in their recorded transactions, but they shouldn't delude themselves into thinking that they are invisible, un-traceable, or otherwise hiding their identity nearly as well as an all cash transaction would.