Hey there tasanhma,
Having an incorrect name displayed in Family Sharing settings can be the result of incorrect information entered in the contact details in the Contacts app.
To help isolate the behavior, review the contact details for yourself and your daughter in the Contacts app on each of your devices. To do so, take the following steps:
- Open the Contacts app
- Locate your "My Card" contact to view your data
- Ensure the details are correct
- Locate your daughter's contact card to view the data
- Ensure all details are correct
- Visit iCloud.com and confirm the contact information is synced correctly there after signing in with your Apple ID
If the issue continues after taking the steps above, then reach out to Apple Support directly. They'll be best equipped to investigate the behavior should it continue. You can use the following link to reach out: Contact Apple Support
Kind regards.