This is likely to have been suggested on previous threads, but if you order online via the GRO website and specify only the father's name, if this does not match, your money will be refunded, so you will not be out of pocket.
If that happens, you can try reordering with for example, mother's name only, and so on, using a process of elimination.
As already pointed out, they won't issue the certificate if only one thing does not fit in with what you have specified, eg, spellings slightly different. That is why the less information given is generally better. You need to use the exact spellings and details as given in the GRO index even if you believe them to be wrong.
Good luck.