The name is nihilism. Literally, nothing could be true.
If 'master signifiers' are empty, as Lacan insists, and language is entirely conventual, then no statement has a fixed meaning, and the meaning of any statement can simply change, in the sense that it will begin having different psychological effects. We know that it will only change into something to which the users can adapt, but it is unanchored and will not stay fixed. The collection of such statements make up a composite theory of effective statements, that will create approximately the intended effects on a listener.
Since their agreement or disagreement is relative to the current composite theory and the theory is going to be superseded continually, any effective statement will have at least some edge cases where it will be wrong, even when it is made. To the extent the next not-yet-known theory is equally both true and false, if likely to be closer to reliability, you can claim all the approximations are all false.
Being able to interact productively with others by using effective statements can still be considered knowledge. It is not 'justified true belief' but it is 'memory with effective power'. (The former standard fails anyway. To the degree you know steps to a dance, or when to say the pledge of allegiance, or you know the 'effable' names of various people's cats, you have knowledge. And those are the latter, but not the former.)
From that point of view, if you take some Platonic or Aristotelian definition of the word 'true', you could argue that nothing is thoroughly/permanently/completely true. But it involves starting out from two different extremist positions, demanding the truth is classically absolute, while the mental contents that statements are made out of is conventual and adapting.
This makes no sense, really. If you know the meaning of true will change, why not give it a useful definition? In the Wittgenstein sense, doing otherwise is a pointless word game rather than a meaningful language game.