I'm changing the wording of your question.
Does the variable that represents the values in the domain always have to be called x, and does the variable that represents the values in the range always have to be called y?
The answer to this (and the reason why) is the same as for the following question.
Do boys always have to be named Jack, and do girls always have to be named Jill?
Here's another hint: If I plot the height of a baseball as a function of time, then I will label the horizontal axis as the t-axis, and I will label the vertical axis as the h-axis.
Points on this graph will have (t, h) coordinates.