What's the problem?

It is impossible in JIRA to restrict issue access to the employees of particular company. It is because JIRA doesn't know what is a "company". There is no such entity.

Existing solutions

As a workaround you can try to use Zones plugin. However, it implements "company" entity as JIRA group. But it complicates managing companies and doesn't give you a full-value entity of a "company".

Solution using CRM for JIRA

If using CRM for JIRA you can configure a company dictionary in JIRA. That will allow you to define a Company in the issue custom field mannually, or auto completing it by issue reporter.

To resolve the access problem you need to add unique security level principle Company People to your Security Level Scheme:

After that all people from the same company will be granted to access issues.