Some names end in an 's' like James and the plural may be pronounced as Jameses abbreviated to James's or James" where an apostrophe is need; this does not denote possession but deletion of letters
[rare moment of pedantry]
I'm not convinced that you are are correct with James''. A single apostrophe indicates the deletion of one or more letters.
Examples:
o'clock from
of the clock
fo'c's'le or fo'c'sle from
forecastle
Two adjacent apostrophes is more commonly known as a quotation mark, inverted commas or a speech mark.
The plural of James is Jameses so a car belonging to them would be written as the
Jameses' car. It could be a clumsy pronunciation but it is unambiguous.
I've not read any style guide that advocates the use of a pair of apostrophes. Though I would love to be proved wrong about their non-existence.
[/rare moment of pedantry]