Consistent masking of denormalized columns?

In an oversimplified example, I have a table PERSON, which has an PERSON_ID, FIRST_NAME and LAST_NAME columns.   I have another table, populated by business logic that contains a number of columns, which include FIRST_NAME and LAST_NAME, but not PERSON_ID of course.

What technique should be used with data masking to ensure that the masked FIRST_NAME and LAST_NAME columns in each table are consistent?   I don't want to mask Doug to Bob in one table and Doug to Fred in another.

TIA,

Doug