Consider the following exchanges:
[1Q]: Is E̲x̲x̲o̲n̲ your parent company?.................. [1A]: Yes, t̲h̲a̲t̲ is our parent company.
[2Q]: Is y̲o̲u̲r̲ ̲p̲a̲r̲e̲n̲t̲ ̲c̲o̲m̲p̲a̲n̲y̲ Exxon ? [2A]: ?Yes, t̲h̲a̲t̲ is Exxon.
[3Q]: Is A̲l̲e̲x̲ her father?......................................... [3A]: Yes, t̲h̲a̲t̲ is her father.
[4Q]: Is h̲e̲r̲ ̲f̲a̲t̲h̲e̲r̲ Alex? [4A]: ?Yes, t̲h̲a̲t̲ is Alex.
[5Q]: Is t̲h̲e̲ ̲t̲a̲l̲l̲ ̲F̲r̲e̲n̲c̲h̲ ̲d̲u̲d̲e̲ your roommate? ..... [5A]: Yes, t̲h̲a̲t̲ is my roommate.
[6Q]: Is y̲o̲u̲r̲ ̲r̲o̲o̲m̲m̲a̲t̲e̲ a tall French dude? [6A]: ?Yes, t̲h̲a̲t̲ is a tall French dude.
[7Q]: Is J̲i̲m̲ your name?......................................... [7A]: Yes, t̲h̲a̲t̲ is my name.
[8Q]: Is y̲o̲u̲r̲ ̲n̲a̲m̲e̲ Jim? [8A]: *Yes, t̲h̲a̲t̲ is Jim.
[9Q]: Is M̲c̲T̲a̲g̲g̲a̲r̲t̲'̲s̲ ̲n̲a̲m̲e̲ Jim? .......................... [9A]: *Yes, t̲h̲a̲t̲ is Jim.
[10Q] Is t̲h̲e̲ ̲m̲a̲i̲n̲ ̲t̲h̲e̲o̲r̲y̲'̲s̲ ̲n̲a̲m̲e̲ Bootstrapping? [10A]: *Yes, t̲h̲a̲t̲ is Bootstrapping.
What explains the differing levels of acceptability of the A-sentences in [1]-[10], especially the absolute unacceptability of [8A]-[10A]?
Note that in [8A]-[10A], it doesn't help to replace that by this (imagine the conversation is taking place face-to-face).
A bit of background
Note that in all cases [1]-[10], that could be replaced by it and the result would be an acceptable sentence (except possibly [7], when the it is quite dubious, if not completely unacceptable). I take that to mean that that in each of the A-sentences above functions anaphorically, with its antecedent underlined in the corresponding Q-sentence.
Of course, the characteristic function of that is deictic, but it definitely can at least sometimes function anaphorically. CGEL gives the following example (p. 1507): They had a b̲l̲u̲e̲ rug, but t̲h̲a̲t̲ isn't the color I wanted, where the antecedent of that is blue (they are coreferential, and both refer to the color of the rug).
I think [7] is different from the rest because Jim in [7Q] should really be in quotes. In other words, Jim does not refer to Jim-the-person, but rather to the word itself---in other words, the word Jim here refers to itself. Thus, technically, Jim and that are coreferential, because they both refer to Jim-the word; but perhaps this self-reference of Jim throws us off, because we expect that when the referent is a word, the reference is deictic rather than anaphoric. The following example supports that guess:
Q: Is the Prince symbol your name? A:?Yes, it is my name.
We would still probably prefer to use that (and I would be interested to know why), but it seems to me that it is here more acceptable than it is in [7A]. And my guess as to why is that the words the Prince symbol no longer refer to themselves, but to the symbol that Prince used to use as his name.