Stop dramatising. That really isn't likely to happen. If it did, it won't be because of their name. Identity fraud can happen to anyone. Thieves take opportunities to clone documents and hack accounts wherever they can. Someone having a common name combination would have nothing to do with it. Anything crime related would go off DNA, rather than names. It's really not a problem.
People can change their surnames anyway, so the surname she's given at birth may not necessarily be her surname for life. Giving her an unusual middle name (for example) isn't suddenly going to make her stand out from the crowd, especially as middle names are rarely used. Day to day, she'll just be Emily Surname or, more likely, just Emily. Many people don't want to stand out because of their name anyway. There's a lot to be said for fitting in.
OP should just pick a name they love, as that's far more important than trying to create a name combination that nobody else has (pretty impossible).
One huge plus for 'common' (as in popular) name combinations - anonymity online. You'd have to know an awful lot of personal details about Emily Rose Smith (surname for example) to find the right one online, whereas someone with a 'unique' combination becomes very easy to trace on name alone.
I never understand why people use such silly reasons to try and convince people they need to pick a more unusual name, as there are positives and negatives for every scenario.