The "problem" of naming children as an expat is usually quite complex, but for your actual problem it's fortunately quite simple: yes, it's possible to have the child's British passport contain practically any name you want, as in Britain the naming laws are very lenient. You can also change your child's name (if all parents consent to this) using a deed poll at any time as well, so if the name on the birth certificate doesn't match to the one you want, that doesn't matter at all.
So at any time if both of you (the parents) consent to changing the child's name, you can do that (until her 16th birthday), and that would be reflected in her British passport, and her British "identity".
Her Icelandic passport and "identity" won't change though. This only means that in Iceland, and in countries where she wants to use her Icelandic passport, she will still have the old name. In Britain, and in countries where she is using her British passport, she will be known in her new British name.
This is of course only possible, because in Britain the naming laws are very lenient, and because of the fact that you can also change your legal name quite easily there.
However in countries, where the naming laws are more strict, as an expat you might still be able to name your child to something that would normally be not allowed.
For example in Hungary you can only chose the first name of the child from an approved list, and they are really strict about it. There is a loophole though that can be used by expats: if the child was born abroad, and therefore his/her first birth certificate was a foreign one, then the parent is allowed to keep that name for the child when applying for the Hungarian birth certificate (which would also mean his/her Hungarian passport would contain a name, that would not have been possible if born inside Hungary).
While I'm not sure about Iceland, similar "loopholes" might be present in other countries as well for foreign-born children, who already have a foreign birth certificate.