So? Why don't you simply use your phone number, nobody else has the same one as you. Why would identity be restricted to names?
You do know that multiple people can share a phone number, right?
Not necessarily; for example, people could generate their own UUIDs as identity tokens.
I disagree with this too, because "who you say you are" is not a single thing; it depends on the context, and you ought to be able to control what connections people can make between different contexts.
For example: I might want to give one ID to my doctor, to connect it with my medical records, and another to the DMV to identify me for a driver's license. There is no reason why these two IDs need to be the same: in other words, there is no reason why the DMV needs to verify that "who I say I am" to them is the same as "who I say I am" to my doctor. Or again, if I have to prove "who I say I am" to Social Security in order to receive benefits, that doesn't necessarily mean I have to use the same ID as I use for other purposes.
Of course, some of the reasons I would need an ID are to prove that I have a certain set of rights, as in the Social Security and DMV examples, so whoever I give the ID to has to be able to connect that ID with the appropriate evidence that I have those rights. So my "Social Security ID" would have to be connected to my employment history, or at least to my history of paying into the system, and my "DMV ID" would have to be connected to my passing of a driver's test. But that still doesn't require any single central authority to dispense or verify IDs; I could still generate my own UUIDs for each of these entities and then allow them to link those IDs to the appropriate information. The fact that we allow the government to create one central "ID" for us does not mean that's the only way to meet those needs.
But it loses the connection to ancestors that our current naming culture has. My name (first, middle, last) refers to some of my ancestors. I would not change that name. I have a few screen names that I highly favor and use in emails, forums, and gaming high scores, but I still also like my given birth name for it's genealogical associations that link me to my identity across generations.
Similarly some people's names are chosen for religious associations. In any case, will we abandon our current naming culture in favor of personally chosen names in the style of online identities?