Currently, there is a limit of two hops ("dots") in dynamic expressions for emails. That means that you can display names (or any field value) of records referenced by a lookup field that is directly on the first named entity, such as: {{Entity1.Entity1LookupToEntity2.Entity2Field}}.

But to get to the name you are looking for, you'd need a third one, such as: {{Entity1.Entity1LookupToEntity2.Entity2LookupToEntity3.Entity3Field}}

You need an additional hop get to a human-readable field from that related record - please can we have a more sophisticated ability to add dynamics contact from related records?