To state for what Company you work as a Consultant, you need to connect to that Company. This can be the Company you are employed by as a Consultant or your business name you may use as a Freelancer.
The reason why you cannot just state the name of your Company is to prevent potential misusage. As such, a validation step is included by having the Company account owner approving a connection request.
A connection can only be made to a registered Company. So if your Company is not registered yet, you can just create a separate Company profile, which is always free, and connect to that Company. See here how to create and maintain your Company profile.
In case many Consultants work for a Company it may be wise to appoint a specific Company account administrator who then manages all connections and Membership plans of the connected Consultants.
Consultant and Company account owner is same person
It is of course also possible that a Consultant creates and manages both a Consultant and a Company profile. Please keep in mind however, that you need to use a separate email address for creating and logging into both accounts. Your password and "Contact Me" details for both accounts can be the same (but not your email address used for logging in).