Talking about "functions" when we are actually talking about equivalent classes of functions almost everywhere equal

An element of a $L^p(X)$ space is usually called a "function", and is usually denoted by letters that are used typically for functions ($f$, $g$, $h$, etc.).

It seems to be a harmful heuristic to act "as if" $L^p(X)$ is made of functions, as a function is really something that should give you a value for each point $x$ in $X$. I am aware that it is now common practice, but I am sure it would help to actually introduce an actual name besides "function" to call "equivalent classes of functions modulo equality almost-everywhere". This concept is fundamental, and should be given a proper name. I don't have a proposition for such name, but I kind of wish someone in the past did.