There are three options. Please, see whether any edit option is there on the site. Then you can use it and correct it.
If that option is not there, see what is the last date for submission of the application. If still, time is there you can go ahead and submit a new application with all the details correctly. So that you can appear the examination with this application. The final option is to send a mail to the concerned authorities explaining to them the mistake committed during the filling of application and requesting them to get the name corrected as given the email. Definitely, they will consider your request and allow you for the examination.
Whenever you are doing such an important work hereafter try to be more attentive and avoid serious mistakes so that there will not be any problems like this.After filling the details please go through all the details once and then submit after ensuring all entries are correct.