That's me. I'm quite happy talking to someone whose name I don't know and who doesn't know mine, and am always taken short when they introduce themselves and want to know what my name is. Possibly some of my reluctance is in having a name that most people can't handle unless it's spelled for them: either my French pronunciation is wrong for their English ears, or my French pronunciation is wrong for their francophone ears: but in any case, it's an exercise fraught with embarrassment. But equally, I don't want to know their names either, and only in part because I won't remember them. If they're from work, I'll ascertain it from written record and so learn it that way, at need*; if not, well, what's wrong with two nameless people conversing, even on a regular basis? It's like street names in Tokyo, that the Tokyoites do without just fine. You're the guy at the coffeeshop or the woman who runs the bakery, and that's the street that runs past the conveni or that has the five vending machines on the corner; and since I know what you and they *are*, I don't need a name to designate you or them.
*It's just permissible to call people 'Sara's mommy' or 'Eli's daddy' as long as you say it half-jokingly; but to me, that's the nomination that makes most emotional sense.