Shakespeare "made up" names by taking existing elements of languages and turning them into names.
He didn't pull random pretty syllables out of thin air, smash them together, and call them a name. For example, he "invented"
Miranda from the existing Latin "mirandus".
As for "all names were made up at some point", I am so sick of that argument. Real names aren't made up--they're taken from existing words and elements of real, existing languages. For example,
Alexander was "made up" from the Greek elements
alexo ("to defend/help") and
aner ("man"). Something like Saronia has no lingustic background whatsoever and is, in effect, a random combination of letters.
I, for one, am extremely grateful not everyone feels the way you do.