In v1.9, the FirstName / Last Name fields on the form can be excluded if you don't want the self registering user to set them during registration. This is most useful for the new passwordless feature to streamline the sign up. If this is the case though, then the form will set defaults of First Name = Site and Last name = User.
This is fine, but if the Custom Query matches a record, then ideally it should use the First/Last Name values from the matched record. Only if we are creating a record, then it should use the defaults.
As an additional step, we could make the default First/Last Name values configurable. The same applies to Email address when signing up with a mobile number only.