To transfer ownership of a container you need to be the "Data Manager" of the container, which is indicated by the blue icon as shown above. Enter the container and click "Access", then "Transfer ownership".
There are two requirements to the person/user you transfer ownership to:
The user needs to be registered as a Veracity user
The user needs to be registered with the same company as you. It is not possible to transfer ownership to persons/users outside your company.
If the current owner of the container has left your company, then you need to contact Veracity support to get help with executing the transfer.