Hi Epictetus_,
Thank you for using the Apple Support Communities! I understand your photo is not updating for Name and Photo Sharing in the Messages app. I'd like to help.
It sounds like you updated your photo through Settings > [your name], and your Contact Card was updated, but not the photo for the Messages app. I would like to clear your previously used photos for the Messages app, and start fresh. To do this, open Settings > Messages > Share Name and Photo, then tap Edit below the existing photo. From there, you will tap Edit under your photo once more, then continue to tap Delete on each photo that may pop up, to remove any older photos. Once those are removed, it should take you back to the screen that shows a blank circle. Tap All Photos > select the album where your photo is located. Once you move and scale your desired photo, tap Choose. Select a filter, if desired, and then tap Done. You may be prompted with an alert that asks, 'Use This Photo Everywhere?'. You can choose your preference. Use Messages on your iPhone, iPad, or iPod touch - Apple Support.
Keep me posted on the results. Regards.