Updating "company_name" through the rest-api

I asked a similar question before and received some good answers for updating contacts addresses. However, I am still searching for an answer to the other part of my question so I will format it more specifically here.

I need to be able to update a contact’s “company_name” through the API. This is not part of a company model. Instead it is an “optional_property” when retrieving a contact through the API. It looks like this on InfusionSoft.

I am specifically referring to the top “Company” where contacts may include the name of their business. Since this is not associated with a company model I cannot update it through that.
When retrieving a contact you are able to include {“optional_properties”: “company_name”} as a parameter and it looks like this:

When I attempt to update this field through the API I receive this error:
{"message":"Unrecognized property: company_name"}'

I would greatly appreciate some insight into how to update this field and potentially other “optional_property” fields in the future.