I guess the title just about says it all. And yes, .\, not that obsolete \. thing.
For those who don't know, .\ is a shorthand way of saying "this computer"*see "footnote" in Windows at a logon screen, which comes in very handy when you don't know or care about the local computer name but need to authenticate against it anyway, such as through RDP or scripting against a set of shared local users and passwords or even locally, if you're unlucky enough to have to physically go to a machine.
Does this have an actual name, and if so, what is it? I feel kind of stupid saying the dot-slash thing, which is how I've been referring to this.
*Footnote: As pointed out by @OliverSalzburg , the . is actually the shorthand for "this machine" and the \ serves as a separator between hostname and username when using the [host]\[user] style of authentication against a Windows machine.
No, there is no specific name for that combination for logging on. Many people have their own name for it but Microsoft never gave it a name and no pseudo standard has ever evolved. The use of ".\" was used because it was already used for file system addressing and it made sense to extend it to machine reference. The nearest it ever came to getting an official name is that "." is called "this" but that is quite unofficial.
The "." simply resolves to the local "whatever" in the PATH/URI systems. So on a file system the "." means the current directory, and in the domain field meands the current system. The "\" delimits domain from user, so .\ literally resolves to the current system with the username to follows. If you're looking for a name for the shorthand - we've always referred to it as "localhost" though that's not strictly accurate (in the URI scheme ./ would be localhost).