That's not good as it should just change to the one you want.
Try a soft reboot by turning the phone Off and On.
Does this happen when you try to change ringtones in all of your notifications such as mail and email and incoming calls etc ?
What happens when you go into your sound settings to change ringtone ? i.e does it change and then revert to another or just refuses to choose another stock ringtone.
Perhaps try another route to change your ringtone.
Settings > Apps > Mail > Notifications > General Notifications > Sound > Media (I choose just once as I have zedge installed) > Choose tone.
Try going into Safe Mode which disable the apps you've downloaded and leaves the stock ones working and then try to change ringtone.
If it let's you then an app or launcher you've got is somehow hindering the settings.
Come out of Safe Mode and start deleting your most recent apps one at a time until the situation remedies.
If it continues in Safe Mode then if this was my phone I would perform the following.
1st Turn the phone Off and then from a set series of button presses that takes you into the phones system files clear the cache. This does not delete your saved info.
No remedy !
2nd as a very last resort back up and factory reset. Remove any Sd Card.
No remedy !
3rd Visit a Samsung Service Centre or Samsung Experience Store.
I wish you all the best with this situation.
Current Phone ~
Samsung Note 20 Ultra 5G SM-9820 _256Gb SnapDragon 865+
Samsung One Ui 2.5/ Android 10.