Mosaic will always check for a match or partial match on the Last name field, i.e. a last name that starts with the provided value.
We do this by:
Checking the value provided with the existing last name for a complete match.
Or if the existing value starts with the provided value.
Or if the existing first name starts with the last name provided and the existing last name starts with the provided first name.
The other fields. First name, Gender, and Date of birth will only be used in the comparison if provided.