formula help

I have two contacts on each lead sheet. One is the patient's info and the other is patients representative.

I need to create the rep as a contact, so I use the name field.
I need to create the patient as an account, so I use the company field.

This works fine as long as the user know to fill in the company field with the patients name, however, it would be much easier for everyone, and prevent errors in the data if I could have a text field called patient's name and that field would be used to create the account.

I know that you can't rename the Company field, but wondering if you could create a formula that would automatically fill in another field based on the results of the the first.

So I type in John Smith in the patient name field and the company name on the lead sheet automatically becomes john.smith.

Thanks.