Hello Sienethu33
Yes, their reply is correct, although not very specific. In fact, the same rules do apply as for flight ticket bookings.
The name can contain up to three typos. For example Emmma instead of Emma.
However, from what I have understood, in your case the first name is completely wrong (yours instead of the child’s one) and it can be understood as another person, for example the ticket could be for the child’s sibling or twin. Thus, it is definitely not a minor error.
Emma Walker, DOB 01.01.2012 is not the same person as Emilie Walker, DOB 01.01.2012.
Nicknames are also not accepted.
Working as a ticket inspector, I suggest you to go to the station to request a new family card - very simple. It is free of charge and you will avoid later discussions on the train and possible surcharges.
I leave it up to you, how you decide.
Kind regards,
Roland