What form do we use if my son worked for a company in the UK and doesn't have a tin number?

To clarify, how was he paid? 

It was a direct deposit into his checking account. On his invoices it looks like they paid it through paypal. 

I also don't know what to use as their tin number?

If he is self-employed, then you do not need to include a TIN for the company he did work for on his return.  Instead you will enter his income as business income on Schedule C by selecting the following:

• Federal
• Income and Expenses
• Show More next to Self-Employment
• Start or Revisit next to Self-Employment
• Yes, to you have any self-employment income or expenses
• Enter the type of self-employment work you do
• Click through a few more screens and you will get to a screen that says "Your XX info"
• Click Looks good
• Then you will come to a screen that says Let's enter the income for your business.  It will give you the option of 1099-NEC or Other self-employed income including the 1099K , cash and checks.  Select the one that applies to you and hit continue
• If you do not select one, it will not let you enter your income
• Enter your self-employment income on the next screen

If he had expenses, you can then continue through and enter his expenses for his self-employment income. He does not need a business name.  You can select, I use my own name. 

Thank you so much, Vanessa A.  Looking at the description of one of his direct deposits it states it's an "Incoming Fedwire Transfer", not sure if that makes any difference.  

No, that will not make a difference. You will follow the instructions above provided by Vanessa A.