The speaker asks the listener if they can understand and name their own problems; if they can, the speaker toasts their success.
The central idea of the song is that most people can't see the truth of their own problems' causes.
This idea is introduced before the first chorus. Everyone is "blind in a world of make believe" where people "sing their songs off key" and pretend "agree[ment]" in order to be "discreet". Everyone is playing an elaborate pantomime, where truth (being "on key" etc.) is less important than pretending that everything is fine.
The chorus says that what the speaker cares about - what "drives" them "out of [their] mind" and into the world - is "whatever makes you see". This is in contrast to how the general public is characterized as "blind" earlier on. They want to make people "believe" and thus "forget" the lies they've been acting out. The speaker urges the listener "to conceive / [that] the images they sell are illusion and dream", or "dishonesty". Here the speaker explicitly says that it is imperative to understand ("conceive") that the "world of make believe" pushed by them isn't real; it's just an "illusion", a "dream" that must be seen through and woken up from.
The next non-chorus section explains why it is important to see the truth. The singer croons, "It doesn't solve a thing to dress it, in a pretty gown" - pretending that a problem is something different, or that it doesn't exist, doesn't solve anything. These things must be understood and "conceive[d]" of properly for progress to occur.
And now we can come back to the section you've quoted in the question. The speaker asks the listener if you can "name your demon", and clarifies that they're specifically concerned with "understanding its scheming". They're asking: can you see the truth of your problems ("demon[s]")? Can you see the truth of how they work, and understand how they sabotage your life with their "scheming"? If you can, the speaker toasts you ("I raise my glass and say 'Here's to you'")
For completion, the following verse has a similar idea, only here the toast is to people trying to overcome their demons and prevent their problems from overtaking their lives and "freedom".
I've watched the video linked in the question, though all lyric transcriptions/quotes are taken from here