(a) The commissioners shall present to the secretary of state an application signed by them, which shall set forth without any detail other than the mere recital:

(1) That a notice has been given and public hearing has been held as aforementioned, that the council made the aforementioned determination after such hearing, and that the mayor has appointed them as commissioners;

(2) The name and official residence of each of the commissioners, together with a certified copy of the appointment evidencing their right to office, the date and place of induction into and taking oath of office, and that they desire the housing authority to become a public body and a body corporate and politic under this chapter;

(3) The term of office of each of the commissioners;

(4) The name which is proposed for the corporation; and

(5) The location of the principal office of the proposed corporation.

(b) The application shall be subscribed and sworn to by each of the commissioners before an officer authorized by the laws of the state to take and certify oaths, who shall certify upon the application that such officer personally knows the commissioners and knows them to be the officers as asserted in the application, and that each subscribed and swore thereto in the officer's presence. The secretary of state shall examine the application and, if the secretary of state finds that the name proposed for the corporation is not identical with that of a person or of any other corporation of this state or so nearly similar as to lead to confusion and uncertainty, the secretary of state shall receive and file it, and shall record it in an appropriate book of record in the secretary of state's office.