Hello, and welcome to Apple Support Communities, DialingByName!
From my understanding, you’re sometimes prompted to update your contact’s picture and name when using your iPhone. With the release of iOS 13 and iPadOS, you can now share your name and photo with your contacts that use iMessage. If this only occurs when using the Messages app, that’s likely what you’re seeing. You can read more about it here: Use Messages on your iPhone, iPad, or iPod touch - Apple Support
When prompted to update the contact’s photo and/or name, you can tap “Update Contact…” at the top of the screen. Each time the other party updates their photo or name, and share it with you, you’ll be prompted to update that information. You can tap the ‘x’ on the alert as well, if you’d prefer to keep their photo and name the way you currently have it.
If you’re trying to upload your contacts to Facebook specifically, I’d recommend checking out: How do I upload my contacts to Facebook from my mobile phone or other accounts? | Facebook Help Center | Facebook
I hope that helps, and thanks for using Apple Support Communities. Take care!