The company custom field is a feature available only in the PRO version of the CRM plugin. In order to upgrade your Redmine, please follow the instructions included in this article.
After the upgrade, go to Administration -> Custom fields, Add new custom field.
Adding a Company custom field will allow you to add only companies (not single contacts) to an issue. You might add a contact to the issue and at the same time associate it with the company. In order to add such a field, choose "Issues" instead of Contacts, and pick Company from the Format dropdown.
Please note, in order for the company custom field to work, you should also enable its use in project settings (Information tab, custom fields at the bottom).