Create a text field to store company's name, go to CRM Company field configuration and select recently created text field in "Copy to" field. You can filter records to be copied by using "Copy JQL".
The company name will be copied to text field automatically for issues newly created after this configuration is done. To edit fields in existing issues users will have to update the issues (including bulk edit)
Hide field if it has no value
You can select if you want to show empty Company field or not with the setting Hide field if it has no value.
Autocomplete of Company Custom Field