Why I can't create company custom field with light version of plugin?
Company custom field is a feature available only in PRO version of CRM plugin. In order to upgrade your Redmine, please follow instructions included in this article.
After the upgrade, go to Administration -> Custom fields, Add new custom field.
Adding 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 company. In order to add such field, choose "Issues" instead of Contacts, and pick Company from Format dropdown.
Please note, in order for company custom field to work, you should also enable its use in project settings (Information tab, custom fields at the bottom).