It is essential that there be a 100% match between the name on the passport, the name associated with her TTN (GE in this case) and the name under then to a slightly lesser extent, the name under which her tickets are booked. Her drivers license is secondary and, in due course, you can get that changed.

So, when she completes her GE application in GOES, she should use the name in her passport with everything, including spaces & punctuation duplicated.

Your profile does not show your residence, but some states require that if there is a name change, that must be accomplished with the drivers license authority within some number of days as well. If that is the case in your wife's state, she should get that done so that she is not presenting an "illegal" drivers license to CBP.

I would also use this as an opportunity to clean up any air carrier passenger profiles so that tickets are booked. For purposes of TSA Pre-Check, you will find that there is a higher percentage of clearance the greater the name match. Ultimately, she won't be denied travel and name issues are routine. But, the entire purpose of a TTN is expedited border crossing with the added benefit of expedited checkpoint processing.