Of course there is actually a ".name". I co-founded the company that set it up, and the original idea was to share the second level so you'd get full control over firstname.lastname.name with e-mail forwarding from [first name]@[last name].name. This followed an e-mail service (Nameplanet) we set up when two of us were discussing how we were both basically blocking a whole [lastname].[tld] domain for ourselves.

Unfortunately .name largely proved too hard to communicate quickly enough, and meanwhile it's clear that people for the most part don't mind weird addresses and/or don't have an issue with seeing e-mail addresses as transient. Which I find quite weird, given I've had the same e-mail address for 20 years at this point. Today .name is operated by Verisign, and second level registrations were enabled years ago, and I do occasionally see them, but the original concept really was part of a wave of people talking about "digital identities" on the net that just died off, in part I think because it seems most of the time peoples identity is much more fluid outside of very official circumstances. E.g. you don't necessarily always want your e-mail address to give away your full name, or your name at all, and in the more formal contexts (e.g. work) you often have another e-mail address anyway and/or your e-mail address is not an important element.

Incidentally, in retrospect I wonder if ".nom" or ".nym" or one of the other proposed names would have been (marginally) easier - people often hear ".name" and think it's a placeholder for a name, especially when you try to explain that your e-mail address is [your first name]@[your last name].name. I use my .com of the same format, and it seems to lead to fewer questions than when I also had/used my .name.