The problem would be: a. how do you prevent an unauthorized third party from making an address that looks like or pretends to be an authentic one. b. How do you have one-time use addresses with such a scheme.
1. Vanity address: it takes a considerable amount of CPU time to replicate a long vanity address, and visually you know who you are sending to from the address. See my sig, 14 characters to have your address look like mine. Single address only.
2. Namecoin-style "Alias"->address registration. Single address only, must be created with coins from address to be registered.
Implementation: You go into your address book, there is an option called "register address on network". You press this, it asks you to create an alias that other clients can see to send money to you. If you are not the first, you get an error that the alias is already taken. The alias is permanently included in the blockchain along with some bitcoins you donate as the fee, and then the address book will list all aliases registered to your address. Other Bitcoin clients would have a searchable database of all these aliases to find you as a recipient.
Such a "first to register" alias system could possibly be used to "sign/register" more addresses to be used with the same alias/account, so that any number of addresses can be "looked up" back to the alias.
3. Something more complex. The problem is with any address currently, the sender only knows the address (made of hash+hash), they can't extract any information from that. You also can't put information in that, it would take brute force equivalent to vanitygen. Adding any info (perhaps hash+info+checksum) would make an address longer, and a third party could add the same info as you.
Anything that is simply a "add more information to an address" type system, a third party could falsify. If your ID was "casascius", someone could be lulled into a false sense of security if they were sending to a scammer's "casacious company".