iPhone receiving messages from previously used iphone

Hello, Jgtech1.

In order to best assist you with resolving this behavior, we have a couple of questions first.

1. Are you getting messages intended for your new number or your family members new number on your old iPhone, or both?
2. Are you getting (green bubble) SMS messages or (blue bubble) iMessages, or both?
3. Are you using the same Apple ID on your new iPhone as your old one?
4. Did your family member create a new Apple ID to use on the iPhone once they got it from you?

Also, did you follow the steps to get your iPhone ready to give it away?

Remove your personal information from your old device

1. If you paired an Apple Watch with your iPhone, unpair your Apple Watch.

2. Back up your device.

3. Sign out of iCloud and the iTunes & App Store. 

• If you're using iOS 10.3 or later, tap Settings > [your name]. Scroll down and tap Sign Out. Enter your Apple ID password and tap Turn Off.

• If you're using iOS 10.2 or earlier, tap Settings > iCloud > Sign Out. Tap Sign Out again, then tap Delete from My [device] and enter your Apple ID password. Then go to Settings > iTunes & App Store > Apple ID > Sign Out.

4. If you're switching to a non-Apple phone, deregister iMessage.

5. Go back to Settings and tap General > Transfer or Reset [device] > Erase All Content and Settings. If you turned on Find My [device], you might need to enter your Apple ID and password. If your device uses eSIM, choose the option to erase your device and the eSIM profile when asked.

6. If asked for your device passcode or Restrictions passcode, enter it. Then tap Erase [device].

7. Contact your carrier for help transferring service to a new owner. If you aren't using a SIM card with your device, you can contact them to get help transferring service to the new owner.

8. Remove your old device from your list of trusted devices.

What to do before you sell, give away, or trade in your iPhone, iPad, or iPod touch - Apple Support

Please get back with us with those answers and we will be happy to direct you further. Take care.