Importing csv - data Custom Module data has a lookup field to Contact

Importing csv - data Custom Module data has a lookup field to Contact

Custom module has a lookup field (Firstname + Lastname) from Contact. I have multiple Contacts with the same (Firstname + Lastname) but they are not duplicate records. When I import Custom Module data, it links the lookup field to just one contact. This is understandable because Contacts require (Firstname + Lastname) to be unique. How can I get to link the lookup field in Custom Module to the correct Contact in this situation without fiddling with the names to make them unique?