Use your EIN, as that's the reason you have an EIN - so that you don't have to share your SSN with those who don't need access to your entire life's history. Doesn't matter if your use your name or the business name, as in IRS records the EIN is tied to both.

Carl, thanks for your answer. You've helped me see the value of having an EIN. Until your message I only knew I needed my EIN to open my bank account. Thanks again!

Yes, the last thing you want to be putting on a 1099-MISC that you may be sending out to multiple people you may have never actually even met, is your SSN. If the EIN is misused, then the impact on you is significantly minimized to the business side and makes it extremely difficult to impact the personal side of you as the business owner.