Why do equations typically have variable names like x and y?
In computer programming, we value meaningful names for variables. For example, if I were trying to calculate a square root, I would call the value I was trying to determine square_root, not x. This makes my code easier to understand.
Is this common in math and I just don't realize it?
Well because $x$ and $y$ are short, and mathematicans are lazy. It would be much more work to write every time the name, which is really annoying if you do a lot of calculation.
And math ist very abstract, so meaningful names can't be found everytime, and it is often so that we generalize something, so we just interprete $x$ as something different, and maybe in the new interpretation the old meaningfull name would be totally senseless.