I am creating a child record and the parent record does not have a name field, which causes the internal ids to show in the dropdown. Is there a way that I can A) use a concatenation of a couple of fields or B) change it to another field to show in the dropdown?

I don't think this is possilbe. I've tried to but have never found a way yet. Can you enable the name field and put a WF in place to "calculate" the Name field based on your other fields?