If your son ran a business, he need to report that business on his own tax return.  It does not matter if he receives a 1099 or not.

If you want to avoid a notice from the IRS asking about why you did not report the income from the 1099-K on your tax return, you might consider filing to show you had a business that had that amount of income, then enter an equal amount as a "other deduction" (so the net amount is $0), and call that deduction "Nominee income to [your son's name]".

Since the PayPal account is registered to you, the 1099-K will be issued to you.  If your son earned over $400 in self-employment, he should file his own tax return and report the associated income and expenses on a Schedule C.    The IRS will be expecting it on your return, but if it is his income, it should go on his return.  

You can either not report it on your tax return and if asked about it later, explain that it was not your income.  Or you can report it as Other Income 2x (once as a positive amount and once as a negative amount).  The net result is the same on your tax return.  But be advised, even if you report it that way, you could still receive an inquiry.   

Have your son read this and have him set up his own PayPal account for his business instead of using yours...;)  A Tax Filing Factsheet for eBay Sellers