Define a new field, gNameSelect in your database and specify global storage for it (open field options and select this on the storage tab). You can define this field in any table in your file or even create a new table just for fields like this with global storage. (I'll put it in contacts for this example.) Put this field on your layout and format it with the value list of contact names as you show in the screen shot.
Write this script:
Enter Find Mode  --> Clear the pause check box
Set Field [ Contacts::Contact Name ; Contacts::gNameSelect ] --> gNameSelect must have global storage specified or this step will not work
Perform FInd 
Since you have a drop down list, use OnObjectSave as the script trigger on this field in order to have this script perform automatically when you exit the drop down list.
Set Field [ Contacts::Contact Name ; Contacts::gNameSelect ] -->I can't seem to enter 2 feilds into this bracket.
When Setting up Set Field, there are two Specify buttons that must be clicked. To get Set Field [Table::Field ; Expression], add set field to your script and click the first button (specify target field). Select Table::Field from the list of fields. Do not click the specify button next to the repetition box. Click OK to close this dialog box. Now click the lower specify button (calculated result) and create the expression to the right of the semicolon (;). Do not try to type in the semicolon.