What's the correct term for this analog of cryptography? Suppose there is a communications channel between two parties. Suppose I want to send information through this channel, but I want to make it look like noise. Ie, I don't necessarily want to encrypt it, though I'm not prohibiting encryption - the point is I want to be able to transmit information to someone else such that what is sent across the channel cannot be distinguished from random noise by any potential eavesdropper.

Maybe something like the above is impossible to do "perfectly", but in any case the question I'm asking is - what is the correct term/keywords for problems in the spirit of what I described above?

Is there a mathematical theory of something of this type?
It's not an exact match to your question, but you're probably looking for something in the field of steganography.