You can use the NZ function to handle those NULL values in your joins.
You can edit the SQL code of your Query directly to look something like this:
Code:
SELECT Person.NAME, Person.LASTNAME
FROM Person
INNER JOIN Person1
ON (Person.LASTNAME = Person1.LASTNAME)
AND (NZ(Person.NAME,"X") = NZ(Person1.NAME,"X"));
Just note that it may have unintended consequences, such as if you have multiple "Smith" entries missing the first name, they will all be linked to each other (which could create One-to-Many and Many-to-Many joins).