What is blocking a deictic use of 'it' in this example?

I think "1Aa" is unacceptable on a semantical point of view. It seems awkward to refer to someone's name as being 'right'. In this sentence, the grammatical function of ' Right ' plays the role of a subject attribute, making an improper judgment of value about someone's given name on a right or wrong standpoint. On the other hand, the sentence '1Ab" refers back to 'that'. I personally never understand what that means whenever 'that' is the subject of a sentence. It just seems unclear. Ultimately, 'that' does not tango with 'it' but pairs with 'this'. There is nothing right or wrong about the name Jane. It's as beautiful as mine, yours, this or that name.

Because the thing that's right isn't the name but the assertion. <That her name is Jane> is right/correct. A name alone can't be right or wrong (see Robbie Goodwin's answer), but the relation of a name to an individual can be. "That" is a pro-sentence.

"Yes, it is [Jane]" is correct because it affirms that her name "is Jane", not that her name "is right".