There ideally should be no problem because your father's name doesn't affect the merit list for any Government job that you apply for. So what you can do is get an affidavit dome by any local advocate stating that your Father goes by both the surnames Chauhan and Kumar Singh and both the names belong to him. Then becauae there is a legal document to prove that both Mr. Chauhan and Mr. Kumar Singh anre the same person and you are their son, it will not be a problem.