You need more than one Apple ID. An Apple ID is used for everything to do with Apple (e.g., iTunes, iCloud, this website, etc). But you can use one Apple ID on your phone for iCloud and a different Apple ID for iTunes.
If it was me, I would completely clear the phone you are giving to your son using the instructions in What to do before selling or giving away your iPhone, iPad, or iPod touch - Apple Support
I would then set it up as a new phone and sign in with a new Apple ID for your son: Get started with iPhone, iPad, and iPod touch - Apple Support
You can then have him use your Apple ID for iTunes: see Set up your Apple ID for iCloud and iTunes - Apple Support
That was how it was done before iOS 8. Since then there is a new option which is Family Sharing. See https://www.apple.com/icloud/family-sharing/ and Set up Family Sharing - Apple Support