Adding a tenant's employer to an existing lease

[Kimberley P.]

The tenant in a condo I own just moved in and signed the lease a couple weeks ago.  Now he has informed me that his employer will be paying a portion of the rent and they want to be added to the lease for tax reasons.  There are a lot of rental scams in my area, many involving "companies" that rent for employees (I won't go into all the stories I've heard) so I want to be sure I'm covering all my bases here.

Do I just add the company name to the lease he already signed and have them sign it?  Do I have them first fill out an application?  How can I ensure that the person signing the lease has the authority to do so on behalf of the company so that it is legally binding?  

One of my concerns is I don't want to give the company any rights to have anyone else living in the condo other than the guy I rented to.  

Thanks in advance for any help you can offer!