Is there a record of how "Cymbeline"'s character names would have been pronounced?
In a word, no! John Barton (in his book "Playing Shakespeare") talks about original pronunciation, and I've put a link below to an audio excerpt which gives you an idea of how scholars think that actors in Shakespeare's day might have spoken. But it is all theoretical: obviously, Shakespeare lived long before the age of the tape recorder.
Cymbeline's character names, though tend to be fairly uniformly pronounced. I've put below what is most usual - say it as it's written in the brackets:
Cloten (probably CLOTTEN [to rhyme with "rotten"], though you sometimes hear CLOA-TEN)