Hello all, many thanks for all your replies, I will do my best to answer them!
Carole it has crossed my mind that her name may have been changed, but I need to exhaust all possibilities with her known name first. Good point about the newspapers, I hadn't thought of that.
groom - yes just to confirm Eva was her middle name. We had always understood that her parents were leaving to start a new life abroad and once settled they were going to return for the baby. I do realise that it seems an incredibly young age to leave a baby without her mother although have never really questioned it until now.
The 1939 dob was given by her adoptive father William Taylor. It does seem plausible that it could be an adoption date instead and would explain having two dob's, although I still don't understand why he would use it on the 1939register.
dundee - 3 - 6 mths was what she had always been lead to believe by the Taylors. Yes, Fanny's maiden name was Smith. No further children during the marriage. I have always thought the timing slightly odd, as they were supposedly married for less than 18 months before adopting. It definitely sounds more plausible to have adopted several years later.
avm228 - that's correct - as for confused...

!!