(a) In response to the secretary of state's rejection of or objection to the registration, the applicant may amend, or authorize the secretary of state to amend, the application on reasonable request of the secretary of state or if the applicant considers it advisable.
(b) The secretary of state, on agreement by the applicant, may amend the application submitted by the applicant. The secretary of state may require the applicant to submit a new application instead of amending the application.