I think this is definitely a bug in parseopt. The main cause of the failure you see is the presence of spaces in the args.
Also, it also seems to matter if `"` is the first character of the string or
not.
For example, below works as expected if no spaces are used:
bash-4.1$ ./parseopt_double_quotes -n='Yankovic"WierdAl"'
name = Yankovic"WierdAl"
Run
But it fails if the double quoted part is moved to the beginning:
bash-4.1$ ./parseopt_double_quotes -n='"WeirdAl"Yankovic'
name = WeirdAl
Run
