Hi rachehe!
It sounds like your Memoji hairstyle isn’t saving as expected, and we're happy to help. If you haven’t already, please try restarting the iPhone:
Restart your iPhone
If the issue is still present, please back up your iPhone before proceeding:
How to back up your iPhone, iPad, and iPod touch
Once you have backed up, you can reinstall the iOS software using these instructions:
If you can’t update or restore your iPhone, iPad, or iPod touch
If the issue is still present, try restoring the iPhone to factory settings and setting it up as a new iPhone:
Restore your iPhone, iPad, or iPod to factory settings
If this issue is present after restoring to factory settings, you can contact Apple Support using this link:
Contact Apple Support
Cheers!