I'm going by my out of date rusty memory, as its been years since I've worked in a ticket office, but I think it was only placed after a name if something could have been added to it to make a ticket valid to another location. For example, Purley might have '*' added to it (I don't know whether it has or not, I'm only guessing) to prevent someone adding 'Oaks' afterwards, to prevent someone doctoring the ticket. Whereas somewhere like Doncaster doesn't have another destination with the same name that can be followed by something, so doesn't need a '*' symbol.
I imagine 'Par' is followed by '*' in order to prevent someone adding 'bold', 'k Street', 'tick' or some other suffix.