I have below Record List pulled from the server:

I need to display a person's name (underlined red). In the record list, I have it as an ID. To retrieve info, the ID is being passed to a SOAP service. It does not allow me to use a function or if a client action is created, it can't be used as a function since the SOAP service is a server call. 

Above is a mobile app, btw.

Question is not very clear.

I am guessing that you are trying to make a Soap call from mobile and you can't make a soap from Mobile for some reason ?

I assume Rest should work in Mobile as it is simple Http call, in this case may be we can put a proxy to consume Soap in server and expose it at Rest for Mobile to make use of ?

If that is not what you are looking for can you please provide more Details so that we can understand better

Where is the recordlist being populated from?

At some point you needed to have that come to the client side in a server action. The best is that on that point you send the name instead of the id (or both) to the client side.