Using “would”

That's a common affectation, but technically incorrect. I don't think you can use "would be" without some kind of conditional clause. Perhaps it's a shortening of "I would guess that it's Julia Roberts", which is still not quite right. It should be either "She is" ("That is" if you like) or "If I were to guess, I would guess that she is", which is clearly too much of a mouthful to be in common use. It could also be corrected to something like "That would be Julia Roberts" ... "if she were a foot taller".

The phrases "that is" and "that would be" have a slight shade of difference in meaning to my ear; the context in which I picture using the phrase "That would be Julia Roberts" is if she had previously been a topic in the conversation, and the speaker knows that the person is Julia Roberts. It also seems to have a sort of deadpan, matter-of-fact tone to it, at least in some cases, as in "That would be Julia Roberts (duh, of course)".

From American Heritage Dictionary:

would (wʊd)
aux.v., Past tense of will2.
...
6. Used to express presumption or expectation: That would be Steve at the door.

To sound gay-ish.

Also seems to me someone would say it to sound a little bit snotty, kind of a between-the-lines "duh".

be definitive "Her name is Julia Roberts"

For some reason I imagine this being used as in "THAT would be Julia Roberts" - as if he'd just introduced a lot of other people...

"This is my grandma Jo, and that would be my grandad George" - the person KNOWS that it IS his/her grandma George, but you still say it - I usually say it in this context, when it's part of a list :)

"Would" is a modal auxiliary verb, so it can be used to express doubt or expectation. In the given dialogue, we do not have any information on the inflection of speaker B's voice, so there is no way to determine the level of doubt. In a spoken dialogue, you would hear the doubt in B's voice, if there was any doubt. The fact that there is no explanation point tells me that B is not excited to see Ms. Roberts, and therefore is probably just being pompous.

You should avoid this ambiguity in your own writing. If B is not sure, that should be clear, e.g., "I think its Julia Roberts." Do not use an adverb, e.g., "That would be Julia Roberts," speaker B said doubtfully. Awful.

I think what speaker B is saying could really just imply that 'That would be Julia Roberts if you knew who she was.' Or something to that extent. So the implication has led to the kind of shortened 'That would be me' etc.. Confusing if you think about it.

you can think of 'would' like any English weak verb (verbs whose past tense ends in a dental). The Old English 'wolde' is the past tense of 'will' (want). in the same way, 'should' is the past tense of 'shall,' and 'ought' is the past tense of 'owe.' Are these usages alive and thriving today? i dont know, but understanding them may help you understand the use of would.

Is would / could an auxilliary verb modal or a subjunctive mood?

I think Judy's post above is right on the money. Of course, in the case of "That would be Steve at the door", there's presumption or expectation because the speaker just hears a knock and doesn't know for sure who it is until the door is opened.

I think in the Julia Roberts example, the expectation is, oh, "displaced" if you will. Speaker B presumes or expects that speaker A should already know who Julia Roberts is because of her huge fame.

"That would be Julia Roberts", perhaps with a touch of sarcasm or incredulity, would mean "That's Julia Roberts. Don't you recognize her? What, have you been living under a rock for the past 25 years? She's only the most famous actress ever!"