One option would be to create a new GoDaddy account that is in the company's name (separate from your personal account). Then you can easily move the domain to that account. And once it is in that account, you can adjust the ownership/contact details.
I also have a domain, hosting and email which is under my personal account. I think I can edit and change the personal information on my GoDaddy account. Would it not be better if I change my account details and set company name instead of my first and last name ?
Or is there a separate type of godaddy registration too where account is registered in name of company ?