I guess the problem is that the officials aren't always familiar with the law.
I assume this was when you were registering the birth in the UK.
There should not have been any problem. Whilst the parents names would have to be the names by which you are known (not necessarily those on your birth cert or passport etc.) under UK law, you were able to call your daughter by any names (first and surname) that you chose.
Rather like if anyone now goes to that Registry Office (or on line) they are legally entitled to a certified copy of your daughter's birth certificate, without being required to give their name, prove who they are or say why the want the copy. Its a public record, so available freely to everyone.
