In my opinion, you should do exactly the opposite.
Teach them that variable names are absolutely arbitrary. You can pick uppercase letters, lowercase letters, little icons, or whatever. The only important thing is that two variables with the same name, or picture, or whatever refers to the same quantity.
It really bugs me that math teaching revolves so much about the syntax of things, instead of focusing on what it actually means. I don't deny that doing math requires some sort of formalism - but it should always be made clear that the formalism is just a convenient way to communicate mathematical ideas, and that what's actually important is the idea behind it.
Once you've established that notation is about communication of ideas, not about their content, it follows (and I think they'll agree) that deviating from universally agreed upon notation is usually a bad idea. But not because the math somehow becomes wrong, but simply because it makes it harder to get your point across. It's like inventing your own, private language, and wondering why nobody understands you.
Though I must say that in the case of variables, saying that they should always be given lowercase letters as names is a gross oversimplication. A variable representing a matrix, for example, will usually be given an uppercase latter. The same often goes for points in geometry. So for variables, what we really do is we try to partition the available letters in such a way that similar things can be recognized as such. Sometimes that means using letters that are close together in the alphabet. Sometimes that means using both upper-case and lower-case letters, because we want to emphasize that $f$ and $F$, respectively $g$ and $G$ are somehow related. What should be taught, I think, is to pick sensible variable names, i.e. ones that make the intention clear, not any particular variable names (which, in a given context, might not be sensible at all).