How do you remove a ringtone from being the default ringtone?
That would depend on your phone....general directions are to got Settings-->Notifications--> and set a different ringtone there. More specific directions can be given if you can tell us what phone you have.
You can also go into each contact (on most phones) and set a specific ringtone for that contact, if you want. If none is specified, it will use the default ringtone you have set in your general settings.