It does not matter whose name is on the form to determine whether or not your son is your dependent. Even if you do not elect to claim him on your return, he would still have to mark on his return that he is eligible to be claimed as a dependent if he meets the definition of a dependent.
For the purposes of determining dependency, going to college is considered a temporary absence and he is still considered to be living with you. The deciding factor for children attending school aged 19-24 is usually whether or not they provide more than half their own support. If your son is paying his own rent and buying his own food and other necessities then you would not claim him as your dependent. If he is not, then he is still your dependent.
All that being said, there is a special rule regarding the American Opportunity Tax Credit. If your son is eligible to be claimed by you but is not claimed by anyone, then he can take the American Opportunity Credit on his own return. For more information, see IRS Publication 970. The American Opportunity Credit provides up to a $2,500 credit, $1,000 of which is refundable even if he has no taxable income.
To do this, you could not include him on your own return. In addition to not being able to claim that education credit which it sounds like you are not eligible for, it also means you would not be able to claim the credit for other dependents.
