Why would someone called Anke introduce herself as "die Anke"?
Source: Teach Yourself German pg. 57
It is just a colloquial way of saying it. Much more common in Austria than in Germany though, I think. I would always say "Ich bin die Kathi" rather than "Ich bin Kathi"/"Mein Name ist Kathi".
Kathi, are you from Austria?
If you were a male would you say Ich bin der Hans?
This form is more dialect. But "Ich bin Anke" and "Ich bin die Anke" are correct.
It's common in the dialects found in the south of Germany and Austria. But not Standard German. (I'd use it too though).
I am from the south but I would never use it. Maybe I am just too old for it.