Unlike in many other countries, there's no such thing as a 'legal' name in the UK. As long as they're not trying to defraud someone else, anyone is free to use any name at any time. For example, I could call myself Fred Smith on Monday mornings, Mary Jones on Monday afternoons and President Zee Zee the Third on Monday evenings (etc, etc, . . ). I could also lawfully sign any documents using those names.
Obviously, the 'authorities' like people to use an 'official' name (such as the one on their passport or driving licence) and they can, if they so choose, refuse to accept any other name as valid. (For example, that's what a bank would do).
However, as long as a witness can be satisfactorily identified from the name they've used on their statement (as your partner clearly can), that statement remains valid and any attempt to get it ruled as inadmissible in a court of law seems to be doomed to failure.
Chris