If you you want to change your company's Record Admin you have to be the Record Admin itself or a Team Member with permission.

Click in the menu bar on Your Company

Next, you will open the team members' area

Click on the green box

You can now select the new record admin from your list. The designated record admin can now be assigned with the red box "Make this Team Member the Record Admin":

If you want to assign a Team Member to adjust permissions you can do this via MANAGE PERMISSIONS 

Info: A record admin can not leave the company. The record admin has to assign first a new Record Admin