I'm aware of the names "Archimedes' constant" and "Euler's number" for $\pi$ and $e$ respectively, but these don't seem to be used very commonly. Even in school I remember $\pi$ and $e$ being almost always referred to as "pi" and "e", to the extent that some math students don't even understand what "Archimedes' constant" is despite using it every day.
By contrast, nearly all other mathematical concepts have descriptive names not associated with the symbols used to represent them. Think of the golden ratio $\varphi$, the imagimary unit $i$, Euler-Mascheroni constant $\gamma$, etc.
Are there any specific historical reasons why $\pi$ and $e$ are not named any better than the symbols used for them?
I asked myself this question after reading this joke. If the problem had been instead "Give an example of a transcendental number", then both "pi" and "e" would have been great answers.