Greetings, RBrito68.
I see that there are quite a number of contacts that didn't move from your iPhone 6 to your iPhone 7. I'm happy to help.
About missing information after you restore your iOS device with iCloud Backup -- If you set up your iPhone 7 using an iCloud backup of your iPhone 6, this is the article you need.
Get help using iCloud Contacts, Calendars, or Reminders -- If you're using iCloud Contacts to sync your contacts across devices, make sure your settings are correct.
Sync your iPhone, iPad, or iPod using iTunes on your computer -- If you sync your contacts to your iPhone using iTunes on your PC, make sure all of the contacts you wish to be included in a sync are selected
If the issue persists, please describe the issue you're facing in greater detail. Include any messages you may have received. The more information you provide, the better chance we will be able to offer some additional guidance.
Take care.