I often attack problems on two levels, a verbal level and a visual level. At a visual level, I try to imagine how everything is related - I arrange the ingredients of the problem into a two (or sometimes three) dimensional configuration - sometimes even a movie.
I then try to reason about the configuration verbally. Like: 'Since $A$ is a proper subset of $B$, I can find $b \in B$ such that $b \notin A$. Fix any such $b$.'
However, the verbal approach suffers from the following problem: I can't distinguish $b$ from $B$, because they both sound the same, 'bee.' So I need to actually visualize those glyphs - I need to visualize $b$ and $B$. But this visualization of glyphs then interferes with the previous visualization whereby the ingredients of the problem were organized into a spatial configuration. I can't keep both images in mind at the same time.
My general question is: What can be done about this problem?
More specifically: Has anyone bothered to come up with letter names that distinguish between lowercase and uppercase? I mean, we could say 'little bee' for $b$, but that's just too many syllables.
Since I was effectively answering the question in the comments, I decided to move it and expand a bit.
What's wrong with saying "small $b$", "capital $B$", "bold $\Bbb B$", "curly/scripted $\mathscr B$", "gothic (small) $\mathfrak b$"?
That's short enough for me (and probably shorter than describing what these letters stand for anyway, and you'll have to do that too).
Should this not match your preferences regarding brevity then -- since I get the impression you are only "visualizing" things for yourself by talking -- you are of course entirely free to introduce some nice abbreviations (e.g. "cap $B$" for "capital $B$"), and/or some conventions (unless I say "cap", the letter is implicitly small).
I hope this is of some help.