To begin with, I do not think that the use of in the first sentence is correct. means how someone refers to him/herself (regardless of how others refer to him/her). For example, means a self-styled musician. (This example was taken form New Century Japanese-English Dictionary.) It is not really about a name, but about a self-claimed occupation or some other attribute of a person. I would say something like instead of in the first sentence.
The use of in the second example is incorrect because (the education system in our country) does not refer to itself as something good.