Please make sure that your table of names includes an ID number and enough other fields to tell two clients with the same name apart from one another. Names are not unique and people also change their names--thus links to other records by name can result in major problems in either the case of duplicate names or name changes.
What you describe is called a conditional value list. The most flexible method is to define a relationship between your two tables that only matches to client records in your Names table. A Quick but much less flexible option is to define a calculation field in Names that looks something like this:
If ( TypeField = "Client" ; NamesID ; "" )
Then base your value list on this calculation field for the first field and include either the Name field or a calculation field that combines the name with other fields such as a phone number, company name, or address. (The added info helps you tell one "John Smith" client from another "John Smith" client.)
If you prefer to use a relationship, see these links for more on the subject:
Forum Tutorial: Custom Value List?
Knowledgebase article: http://help.filemaker.com/app/answers/detail/a_id/5833/kw/conditional%20value%20list