Name for a conversation where two people are talking about two things, without their knowledge [duplicate]

The people speaking are at cross purposes.

at cross purposes

If two people are at cross purposes, they think they are talking about or trying to do the same thing as each other, but they are actually talking about or trying to do different things.

• They had been talking at cross purposes earlier, he realized.

[Collins COBUILD Idioms Dictionary]

at cross-purposes

with opposing viewpoints; with goals that interfere with each other.

• We are arguing at cross-purposes. We aren't even discussing the same thing.

[McGraw-Hill Dictionary of American Idioms and Phrasal Verbs]

The phrases "to be/talk at cross purposes" can be used for this type of misunderstanding.

(The Free Dictionary) be/talk at cross ˈpurposes (of two people or groups) misunderstand what the other is referring to or trying to do
♦ Mary and I spoke about Anne for a minute or two before I realized we were talking at cross purposes: I meant Anne Smith and Mary meant Anne Harris.