Yes, it will be a definite red flag if there is no clear CEO in the company.
However, nothing says these titles have to map in any way to actual responsibilities inside the company. Just make someone CEO on paper, at random if you need to, and disregard the title internally.
However, nothing says these titles have to map in any way to actual responsibilities inside the company. Just make someone CEO on paper, at random if you need to, and disregard the title internally.