My son has a iPhone he is under 13 so he is on my family account but I do not want him having access to my iCloud my purchasing information my photos, my contacts and other such things how do I turn these off

My son currently just got a iPhone X and he has all my family sharing because he is under 13

No, he can share your purchased content because he is in a family sharing group with his own Apple ID or he is using yours - you didn't comment on which of these two possibilities are being used. Being under 13 does not determine sharing ability.

I do not want him having access to my information from my phone such as pictures text messages, purchasing information, my contacts, and other such information

In a family sharing group all this is private and separate. He cannot see the private information from your iCloud account, unless you and he have the same Apple ID.

You and your son should have different Apple IDs. If he does see this data then you and he have the same Apple ID and, consequently, he has access to your account and all its information. If he has a different Apple ID and is signed into this on his iPhone, he can't see your purchase history. He can share your purchased content - apps for example.

how do I change the name on his iPhone

This can be changed in Settings > General > About > Name

Touch on Name and then you can overtype a new name for the device.

Apple has a description on how Family Sharing operates in What is Family Sharing? - Apple Support

Here's a rundown of what Family Sharing is and how it works: https://www.youtube.com/watch?v=I6vZd14FsJ4, here's how to set it up: Set up Family Sharing - Apple Support