If you don't want to use your personal SSN, you can get an EIN (federal tax number) for the business for free from the IRS web site in about 15 minutes.
https://www.irs.gov/businesses/small-businesses-self-employed/apply-for-an-employer-identification-n...
But you do have to provide a tax number to anyone who pays you, and you have to collect a tax number from anyone that you pay.
