- Make sure you have a contact entry for yourself in Contacts.
- Set the picture you want for that. I recommend cropping it OUTSIDE the contacts app, then setting that already cropped picture, as the cropping done in the contacts app never stays consistent.
- In Settings -> Apple ID, set the photo there to that same photo.
iOS/Apple/iCloud uses both in different places. It's not consistent and has changed randomly for me in the past. So making sure you have a contact photo set for yourself, AND a photo set for your Apple ID in settings, ensures that it will appear everywhere.
It can take some time for the change to propagate to all your devices.