No. If you attempt to update your profile, you must choose a user name that's at least 3 characters. The comment system is designed to work with user names at least 3 characters in length. The fact that you were able to get away with this when you initially created your account was a bug. You're required to fix it now, if you make a modification.
The official word is here:
We no longer allow names of 2 characters.
3 characters is the minimum name length, and this is enforced.
However, users who have an existing 2 character name may retain it, but will be unable to copy their profile from site to site until they make their username at least 3 characters.
You had to choose a compliant user name when you created this account on Meta, so it's not clear why you're resisting doing the same thing on Stack Overflow.
EDIT: In contrast to what Jeff says here, balpha says in the comments here that there's a special case in the code that allows @ replies to work for existing user names of under 3 characters (but more than 1). I'm not sure which is correct, as I haven't tested it myself.
But even if it does work, that's a backwards compatibility hack, which is something that we all as programmers should know better than to rely on. When you start making changes to your profile, you lose your "grandfathered-in" status, and have to bring your account up to full compliance. I struggle to see where you think lies the real cost of this change. To paraphrase Steve Jobs:
Just change the name of your account. Not that big of a deal.
As far as why Stack Overflow recently decided you live in Brooklyn, Alabama, more information is available here:
We're doing a best-guess match on locations across the network in an effort to get more consistent location formats for all the users, for example mine would be "Winston-Salem, NC", "City, ST", or "Something, Ontario" for Canada, "London, United Kingdom".
You can update the information now manually, and the system will respect your changes.