paid fellowship

Minimum Gross income for filing status single is $14,600, so he should not have to file.

Yes, your son needs to file a tax return and report the $4,500 of income.  Income reported on Form 1099-NEC is considered self-employment income, so your son will have to report the income on Schedule C.  If he has any expenses related to the income he will be able to deduct that.  If that is his only income, he won't owe any federal income tax, but he will owe self-employment tax, which is basically both the employer's and the employee's half of social security and Medicare taxes - the rate is 15.3% of net profit form self-employment.