If you did not asked for name change during interview and if you are not able to get them to accept that request now (may be via infopass), your only option is to change name via local courts. Sometimes it might be better since oath ceremony with name change can drag on where as name change in local court is failry quick (Case in example, I know a person who is still waiting for judicial oath for more than 10 months since he requested name change during citizenship. If local court name change was opted, this would have been over in 2/2.5 months. This also depends on your DO. Some DO may schedule name change oath ceremony sooner than others)
Once you have certificate, you have two options,
1. Use that certificate to get passport with wrong name. Go to local court get name changed. Then send that name change order to passport office and get passport name changed to new name. There is no fee if you do it in 1 year from date of passport issue.
2. Get certificate with wrong name, do NOT apply for passport yet. Get name changed in local court (2.5/3 month process max) Then submit name change order and Nat cert to passport and get passport in correct name.
Not sure which your DO is and how fast they schedule oaths with name changes. If you want, you can take infopass and see if you can request name change now (After the interview) If they do not, local court option is not that hard.
Hope that helps. Let me know if you have any questions.