To remove a Business Partner registration that was just created and have not been used for any entries or setup, simply use the "Delete" button at Business Partner Registration module.
Note: The loading time for deleting a Business Partner registration depends on the amount of document entries on your database, as the system has to check through every single transaction before the deletion can be completed.
If that Business Partner has been used before, it cannot be deleted.
Instead, Edit that Business Partner, and remove the Customer and/or Vendor group selected.
When a Business Partner does not belong to a Customer or Vendor group, it is neither a customer nor a vendor, hence cannot be selected at documents on either Sales or Purchases activity.
Refer to the field "Available: " as an indicator.
There is also an "A" column on the module, so users can tell at a glance if a Business Partner is available (for selection in document entry) or not.