I will advice you to contact your college or the concerned university to correct your name. A error in name is a serious problem It will not only create a problem only in govt job, but also create a problem in any private job or any kind of legal procedure. It may take a little time so apply it now.
If it is not corrected you may got stucked in the document verification phase. So, do it as early as possible.
You can produce the photocopies of your photo identity proofs to specify the correct name while submitting the application for the name change. You may write an application in your own hand or sometime they have a certain error correction form to correct such errors; if they have such forms just fill it and submit with supporting documents.