Your instructor is both right and wrong.
Yes It could be a problem but not with an examiner. Most applicants are so nervous they can’t remenber their name let alone write it.
Point is there may or may not be an underlying medical problem that could potentially be disqualifying for a (first class) medical.
You doing this for giggles or as the start of a career?
Friendly word of caution here: the FAA doesn’t take very kindly to “omissions” on a medical application. Unintentional or not.
I’m getting the feeling you didn’t discuss this with your medical examiner.