The name of a limited liability company following reinstatement shall be determined as follows:
(a) If the limited liability company remains in the Secretary of State’s records as a limited liability company which has not been dissolved, then the name of the limited liability company following reinstatement shall be that limited liability company name at the time of reinstatement.
(b) If the limited liability company is listed in the Secretary of State’s records as a limited liability company that has been dissolved, then the name of a limited liability company following reinstatement shall be that limited liability company name at the time of reinstatement if that limited liability company name complies with Article 5 of Chapter 1 at the time of reinstatement. If that limited liability company name does not comply with Article 5 of Chapter 1, the name of the limited liability company following reinstatement shall be that limited liability company name followed by the word “reinstated.”
(c) A limited liability company shall not be required to file a statement of dissolution in order to retain or obtain the name of the limited liability company.